In general I am not seeing adult beginners in their first year on a horse competing in shows. It’s different for little kids; as I mentioned below there are even classes for little kids who can’t ride yet. As an adult, I think it’s reasonable to postpone showing until your skill levels are more on a par with your other adult competitors.
The wonderful thing about horseback riding is that it is part of the category of “joy in movement” sports that can be wonderful without any thought of competition. Sports that require a lot of skills but also have a lot of intrinsic reward.
In this way, I would lump riding in with skiing, skating (in places with outdoor frozen lakes), sailing, cycling, snowboarding, skate boarding, swimming. You can do all these sports at a very competent level for your whole life without needing to compete, or anyone asking you if you plan to compete. And indeed the bar for competition is quite high. You need to be a really good swimmer or skier before you compete.
This is different from team sports and racquet sports where there is no point mastering the skills unless you like and want to play the game, and there are all kinds of beer leagues and workplace teams that can accommodate almost any skill level as long as you have a good attitude… Or the very isolated track skills like shot put and javellin and long jump that you’d only master with plans for competition.
So probably most riders take enormous pleasure in being on a horse but show rarely or never. You need to discover what gives you pleasure. Is it cantering on a trail? Learning subtleties of dressage or reining? Mastering obstacles in trail class? Etc.
Remember that competition boils down hundreds of hours of prep into a crucial 5 minutes in the arena, and measures only a slice of your ability. If you like to win and you do win, that’s a tremendous emotional boost! If you like to win and don’t, not so much. If competing makes you physically ill or you don’t have that much invested in winning, it may seem like a poor investment of time and resources.
That said, many if not all sports programs for children are structured around either competition or tests and badges, because many (not all) children seem to respond well to external motivators (they are taught to do so in school). And competition is very motivating for many parents who see it as an objective measure of progress. It also helps develop the corporate identity of the program ,(“team spirit”). And absolutely it is s revenue generator for lesson programs.
OP if you are an adult beginner in a predominantly junior barn, it is likely that competition is stressed more than it would be if the barn was full of adult beginners. Also there will be a graded level of show classes available for children whose parents want to pay, from cute leadline and walk trot classes on up. Even a child that can’t really ride yet can find a class.
I was a self directed self taught kid in an era with no programs, and went along to the local playdays trying everything out on my all round pony, and getting lots of 3rd and 4th place ribbons. I wasn’t very invested in this, and the cost was minimal. There was a strong social component. What I really loved was back country trail riding and galloping fast, especially when you could combine the two 
I returned to riding a decade ago, and I would finally say after years of lessons and effort that I am a decent rider again, but with less bravado. I haven’t shown, there hasn’t yet been a time when that has made sense as something to do. I’m not writing it off for the future. But I find that as an adult, I don’t see the point unless both me and my horse have something to show off, and we aren’t at that stage.
I also feel like my job is deadline and goal driven, and requires constant assessment of others and myself. Maybe if my job was softer I would crave more structure and a graded system in my leisure activities. At this point, though, it feels like it would be overload to be competing in my leisure activities too.
I also think showing is fun for people because it gets them off the property. I have my own trailer now and go out for trail rides, back country or less strenuous usually with a friend and a picnic. That gives us a sense of new challenges and accomplishments too.
