Since you mention koans I will answer this from the perspective of Zen Buddhism (or chan as it was/is called in China).

The short answer is that in the history of Chan/Zen in China and Japan it indeed was mostly ordained monks who practiced meditation but there was some lay participation. I will describe those briefly and then describe how and why these practices took hold in a big way in North America and Europe among the laity.

The Buddha was a renunciant who "left home" to pursue a life of spiritual advancement. Ascetic renunciants were an aspect of Indian culture from at least 1000 BCE so it was embded into that culture from a philosophical and social perspective. The Buddha (or perhaps his descendants) begun a formal order where someone vows to take refuse in Buddha, Dharma (the teachings) and Sangha (buddhist community) to become an scetic renunciant. A key part of this process is the the monk vows to live their life based on the rules of the Vinya which is a set of rules for monks. This vow is called "taking the precepts". They did this because the belief was that by following the precepts you 1) increase your chances of becoming enlightened in this lifetime and 2) generate merit which will improve your chances of a favorable rebirth in the next life in case you do not achieve in enlightenment in this one.

The basic social contract between monks (I'll use the term monks for women and men) was that the monks worked towards enlightenment and the laity supported them via donations to increase their own karmic merit.

So when Buddhism was brought to China this basic pattern was kept intact. Individuals would ordain as monks and laity would support them to earn merit. Additionally laity would often engage with Buddhism by chanting in order to earn karmic merit and also they would participate in ceremonies such as ones designed to honor or placate deceased ancestors.

As in India its mostly ordained monastics who engage in meditation practices. There were some notable exceptions. Lay practice in general was in fact an understood possibility. One of the most influential scriptures in Chan/Zen was called the Lankavatara Sutra which stars a superstar layman from the time of the Buddha himself. There was also famous stories about a lay Chan/Zen practitioner named Laymen Pang who was another superstar enlightened non-ordained practitioner.

Aside from these semi-legendary laymen there was in fact some real life laymen who practiced meditation in China. One of the ruling classes in China were what we call the Literati. This highly educated member of upper class society were the dignitaries and administrators who ran the machinery of government. This group took a special liking to Chan/Zen. In fact we only know of the teachings of some of the central and most famous Zen/Chan masters from the Golden Age of Chan because certain Literati choose to edit, publish and popularize their sermons. Many of these Literati would become students of the masters and practice meditation. You can also find letters written from Chan/Zen masters to particular practicing laymen and giving them advice on meditation practice and spiritual development in general.

What you dont see however is any of these laymen becoming "Dharma Transmitted" Chan/Zen teachers themselves. This lineage of spiritual/political power was kept firmly within the ranks of the ordained clergy.

Once Zen was transmitted to Japan you find the basic pattern continuing: meditation being primarily an ordained monastic experience with some lay exceptions. Perhaps the biggest exceptions was the the 17th century or so where a few particular Zen Masters such as Bankei and Hakuin became extremely popular among lay people and a considerable amount of lay people (men and women) would take up meditation practice inspired by these populist teachers.

Looking at the history of Zen in Japan, by the late medieval and earn modern period you find the situation where every village has some sort of buddhist temple. Most of these temples are not monastic training centers but rather smallish affairs where priests become residents and administer to the spiritual needs of the local population. To be the "abbot" of one of these temples you need to be certified as a "dharma transmitted" member of the lineage that legend has it goes all the way back to the Buddha. These priests would have various levels of genuine spiritual aspiration and usually only participated in intense ascetic meditation practice for a few years in their late teens and early 20s. After this they would receive dharma transmission and become a local parish priest.

The open secret was that many of these priests did not live as what we would consider ascetic monastics once they were done with their initial training. They participated heavily in worldly affairs and were often landlords to tenant farmers as temples frequently had considerable land holdings. Another open secret was that many of these priests had unofficial wives that didnt get seen much in public.

During the Meiji Era (October 23, 1868 to July 30, 1912) the government legalized clerical marriage and the wives stopped being unofficial. Most priests would end up getting married and parish temple abbotship quickly became hereditary.

The point of describing this history is that when Zen teachers started coming to america in the mid 20th century the model that many americans saw were "monastics" who lived lives that didnt seem terribly monastic. They were professional clerics that got married, had families and were very much part of society. They were not renunciants who lived ascetic lives 24/7 focused on spiritual practice. In fact, possibly one of the two Japanese Zen masters who were most influential in transmitting the religion to Japan was named Yasutani Roshi and he came from a fairly new zen sect called the Sanbo Kyodan that explicitly focused on lay training. It was the first Zen lineage where the Zen masters themselves could be laymen.

By why was it mostly laymen in america who were interested in Zen in the first place? A big part of that answer was how Zen was first publicized in America. The first popularizers were two authors named DT Suzuku and Alan Watts. The way they presented Zen in their books was a tradition of direct-experience that forsook the constraining and conditioned dysfunction of regular society and existence and allowed one to live a natural, dynamic life. This philosophical view was extremely influential and popular among beatniks who in turn were extremely influential to the emerging hippy youth culture. Zen (or at least what was seen popularly as Zen) rocketed into popularity among a large, eager lay audience that quickly started acclimating all sorts of eastern practices, including zen.

So you had a large lay audience, being taught either by lay teachers or ordained teachers that lived largely "lay" lives. It became natural that a large percentage of zen practitioners would see the practice as relevant to how they lived.

Another reason meditation in general has worked itself into popular culture is that medical professionals are able to some degree quantify the actual efficacy of the meditation practices. Brain scans show meditation changing the brain for the better. This has mostly manifested in the extremely popular mindfulness movement and has also merged with alot of yoga practice. Many yoga teachers include mindfulness language and philosophy in how they teach yoga.

If you have any questions about sources, please dont hesitate to let me know specifically what you are interested in and I would be happy to share.