Okay, in order to answer this, I may need to do a bit of a road trip through history, potentially splitting it in two answers. So heads up, this could be massive.

Let's start with a small excursion into mental health, the history of mental health, and the theory behind the development of the American Prison and Asylum culture - both are inseparably connected and vital to answer your question. You will see at the end why. And then, since it's practically interwoven with this part of American history and historical medical architecture, I will introduce you to the wonders of the Dr. Thomas Kirkbride buildings and his Theory of Psychiatric care that was pretty much the reason for the entire phenomenon of these gigantic Asylum buildings more or less unique to America. I will take a well documented Asylum with a famous history and plenty of documentation in media and film as my example to illustrate all of this, the Greystone Park Psychiatric Hospital, which stood in Morris Plains, New Jersey, from 1876 until it was demolished in 2015, so you will have a chance to find good documentation of it all beyond the sources I will provide.

Now, I will start by stating that this has little to do with any form of conspiracy; the reasons for the locations and choice in materials for these buildings were rooted in the theory behind the architecture, but more about that later. The important part is how mental health has been viewed prior to these asylums, and for that, we need to start with a look into how the mentally ill were treated prior to the 19th century.

Asylums, as we understand them today, have not been a thing up until very recently, historically speaking, but mental illness and the idea to contain people suffering from them somewhere out of the way is ancient. Literally. For a very long time in medical history, basically all of European theories about medical knowledge and the reasons for disease was based on a ancient theory about the four bodily fluids or humors - blood, yellow bile, black bile, and phlegm. Health was dependant on the balance in which these fluids operated with each other in the body; and the type of disease, so the theory, basically was dependant on which of these fluids was out of balance. This theory reaches as far back as to roughly 400BC, and found one of its founding father in Hippocrates. Prior to this theory much of disease was blamed on supernatural reasons, but with the development of medical theory, this changed. Now, Mental illness was a topic even back then - it's been for as long as humanity is alive. And Hippocrates in particular, blamed what he understood as mental illness - separated in epilepsy, mania, melancholia, and brain fever - also on these fluids. This theory remained pretty much unchanged right through up until the 19th century, but while Hippocrates was of the opinion that mental illness was not shameful, or a punishment from the Gods, but a disease a patient could not be blamed for, many others during the centuries after him had other opinions.

For the longest time individuals showing behavior outside of what people understood as normal where regarded as shameful and often outcast or hidden. This was a fate not just for the mentally ill, but also for the disabled and physically invalid. There also was no understanding of conditions such as Depression, or Psychosis, and no such thing as trauma recognition or PTSD - the last one being only recognized as a real thing less than 100 years ago. While it would go beyond the point here to elaborate the destiny of these people prior to the 17th century it detail, it can be summarized by saying that the Catholic church may have preached about generosity towards the poor, but had little to no mercy for the mentally ill. A great number of witches and possessed people during the 12th and up to the 15th century, but especially women, may much rather have suffered from mental illness than from a visitation of the devil. And prior to that, people who where outcast of the community due to not fitting the norm, may have suffered similar fates as superstition and curses etc. dominated a lot of the folklore and understanding of the reasons for disease and disorder. With the start of the 16th century, there begins to also be documentation of privately financed buildings to contain and collect the abnormal; however, this not just invovled the mentally ill, but the poor, disabled, and unwanted. Most of these people died uncared and unwanted, in what we came to call the Madhouse. You must understand, however, that again, there was not the same idea of disorders as today, and pretty much everyone unwanted could end up in such a institution. There was no medical personal, no care, and nobody who fed or clothed these people - the most simple idea behind a madhouse was to contain and separate the undesirable portion of society from the rest. Remember this part, it will become important later. Famous examples to read up on here would be Bethlem, or Bedlam, in the UK, which, during the 17th and 18th century, even opened it's doors for the public to finance themselves, having much more in common with a modern zoo that you paid for a visit to, than with a hospital.

So, the first madhouses that turned into hospitals or asylums had little to do with a modern hospital or psychiatric clinical enviornment. People were chained up, if they were regarded dangerous, locked up, kept in their own filth, and exposed to very experimental treatment methods. While prior to the 16th century it was mostly the church or private sponsorship, even a number of Crusaders amongst them, at this stage it became a matter of the state to contain the insane and undesirable, and often public shows of the insane a way to finance them. People were imprisoned there, and it was not common to get out of there again. Once in there, the great majority died in there, and ended up buried somewhere in a poor people mass grave. Also important here to remember later. The insane had pretty much no human rights left; in fact, they had little to no humanity left - and there was little to no drive among medical professionals to treat them. The favorite means to keep them under control, much like animals, was installing fear in them and herding them around or looking them up.

Why is this important? Now, it is important, because the dawn of the 18th and 19th century changed everything. At this point there was a change in society, away from treating these mentally ill people like animals, with no human qualities, towards the understanding that these people were actually ill and treatable, to some degree. In the late 18th century, here and there, some doctors started to remove the chains from their patients and instead began to give them a more humane treatment, more hygiene, and more freedom of movement. The times in which they just basically shat below themselves and sat in it much to the amusement and awe of paying customers were not over just yet, but in some hospitals things started to improve thanks to the early symptoms of the European Enlightenment movement and the dawn of what we regard as medical science today.

And this is pretty much where we can switch over from Europe towards America, because this is where the Asylums you are wondering about come in. Not just yet, but this is where the idea of change starts.

EDIT: typos

Thank you for bringing this question over from r/Lost_Architecture, I think you'll get more answers here.

The short answer is this: The Industrial Revolution created the need for large asylums, a need that hadn't been there before. The US in the 19th century started out as a much more agrarian society, with cities having relatively lower populations. Families often lived on one homestead or in one town, and there was a lot of familial interdependence, whether it was nursing the sick, care during and after childbirth, or extra help for bigger projects. Even if a family wasn't strictly agrarian there was interdependence. This also provided a way to manage mentally ill family members. I say manage because there was really no treatment to speak of. Families of the mentally ill had to manage the symptoms. They were left to cope with an individual's particular symptoms, but in cases of severe illness, there was not much more they could do beyond confinement. A space was created where the individual could be confined and family members could try to provide basic care. It was not really a great outcome but at least the problem was managed.

This all changed with the Industrial Revolution. Industrialization changed the geography of the country. For reason probably better explained by an expert in the Industrial Revolution, there was a huge influx of people coming into cities to provide cheap labor in the many factories. Because the laborers were just that - cheap - people were forced to live in smaller family units crowded into tenements, with multiple family members (even children) leaving the domicile to work elsewhere. Mentally ill family members who would have been previously manageable were manageable no longer. They weren't even confinable. The result was the over-utilization of poorhouses and an overwhelming of the prison systems at the time. This left families and, more to the point, local government, with a big problem. These were not designed to house the mentally ill but there was nowhere left to put them. The burgeoning middle class also struggled with how to manage mentally ill family members within their households.

Sanatoriums - hospitals for the mentally ill - did exist prior to the turn of the 19th century. But they were generally out of reach for all but the most tremendously wealthy. Public asylums did exist in Europe. They were not always models of mercy, with some even selling tickets so that people could come to laugh at and taunt the residents, but they did manage and confine the mentally ill. By the mid to late 18th-century humanitarian reforms improved the conditions of asylums, and soon the first public mental hospitals were being built in the United States. But they were often small and were generally quickly overloaded.

With an important nod to other reformers like Dorothea Dix, enter Thomas Kirkbride. Kirkbride was a physician who felt that the environment of a mental hospital could in itself aid treatment. He believed that things like open space, exposure to sunlight and fresh were absolutely critical to the care and treatment of the mentally ill (note the change from management and confinement). Kirkbride created what is known as the Kirkbride Plan. In the Kirkbride Plan, hospitals were very large structures. With an administration building in the center, patient wings extended out on either side, with each housing one or more wards. Because the circulation of fresh air, more open space, and exposure to natural light were so critical to his theory, Kirkbride Plan hospitals were very large. Just as important as housing patients was how they were housed. Care was given to interior design and ward structure and there was even a supportive landscape architecture plan. It called for large, well-maintained lawns and grounds - sometimes maintained by patients. There would even be satellite buildings where patients could work - hospitals could run their own cottage industries.

This plan was met with enthusiasm. Almost 75 hospitals were built using the Kirkbride plan from the middle of the 19th century to just after the turn of the last century. A few were built on the west coast, but they were concentrated in the Eastern third of the country. They began to wane in popularity because they required huge amounts of funding and like many social programs, funding gradually became inconsistent.

Sutro Baths in San Francisco and The Moorish Baths in Montana, however, were not mental asylums. They were public bathhouses, both large and quite beautiful, but they did not function as hospitals for the care of the mentally ill. But beyond that, these State Hospitals were vast complexes with grand buildings not because how many patients lived there but because of how they were designed to treat patients. Though many did become overcrowded with time.

On a personal note, my great-grandmother was briefly a patient at the first Kirkbride Plan hospital, Trenton State Hospital, before being moved to a tuberculosis ward at Torrance State Hospital in Pennsylvania.

For those interested, the book Asylum by Christopher Payne is a stunningly beautiful book of photographs of the crumbling Kirkbride Plan hospitals.