There are fashion based reasons (JFK stopped wearing hats, for example, which has oft been attributed to the start of a trend), but mostly it comes down to practicality.

Compare life in 1850 vs. 1950 to give a sense of the role of hats in daily life.

In 1850 people are traveling by foot a lot. They're walking to/from work or school. They're waiting outside at the rail station for long distance travel. They're riding a horse or a wagon. They're spending a lot of time exposed to the elements including the rain, sun, wind, dust, etc. They're spending maybe hours a day outside every day. In those circumstances you need good outdoor gear. Warm clothes, good shoes, a sturdy overcoat, and a hat or hood. Without that you're going to end up cold, wet, sunburnt, covered in dust and dirt, or if you're very unlucky all of the above. In that environment hats are not just practical they're a necessity. Going around without a hat means subjecting yourself to one hardship or another most days of the year.

In 1950 hats are still practical, but much less necessary, and linger on in their ubiquity mostly due to fashion. Whereas in 1850 people were traveling around often exposed to the weather, in 1950 that's far rarer, largely due to the rise of the automobile. People aren't usually walking miles per day for their commute, they're taking a car, or a bus, or a taxi, or a train. They aren't walking to the shop, they're taking a car or public transit. They aren't riding a horse or a cart to travel between cities, nor are they even walking several miles to a train station. Additionally, any vehicle or building they enter isn't just a structure, it'll be heated, windproof, etc. This makes it a lot less of a hassle to be temporarily exposed to the elements without a hat. The important thing to note here is that even if wearing a hat is of marginal utility 99% of the time, if it is of high utility 1% of the time, and you can't easily predict that 1%, then that incentivizes wearing a hat all the time. Today or in 1950 being in a situation where you'd have to walk 5 miles in the pouring rain counts as something of a personal emergency, whereas in 1850 it would have been something you'd have expected to just have to do from time to time.

At some point people stopped routinely encountering the conditions that made hat wearing such a necessity, and then eventually it just fell out of fashion.

Not to discourage any new answers, but I think you'll find this thread useful:

When did men wearing hats become so universal and when did it cease?