If you really want to process colour film at home, there's nothing to stop you. Formulae for the colour processes are easy to find, if you want to do everything yourself from scratch. Or you can buy kits. You can even adjust the colour balance of slide films, and do clip tests.
I've processed colour slide films (starting in 1968), and made Cibachrome prints from slides.
BUT personally, I derive zero satisfaction from pouring liquids into and out of a light tight container for an hour or so. I'd rather be using a camera or being creative in making a print. And also personally, I don't find colour photography particularly satisfying or (to me) a very creative process. I am prepared to concede that the extra scope for creativity that comes from having camera movements available could make colour photography of limited interest to me, other than purely as a recording medium.
Finally, for me, a print from film has a quality that one from digital does not; and that ultimately is why I use film. Developing films, messing around with formulae, getting involved with what to me are unnecessary complications like the zone system that fix problems I don't have, all that is drudgery I could do without. I have only one reason to process my own Black and white films and that is that trust myself and not the postal system. The only times I have had Black and white films processed for me, I have used a local lab that I can hand the film in to, and collect a hour or so later.