As someone who was scared to dip into competitive until recently, let me give you my take. Context: I'm not very good at this game (except Mercy, I am good at Mercy), I've never taken a FPS seriously before Overwatch, and I have have general performance anxiety such that I've left a speech to cry before.
"3 times since Overwatch launched I’ve gone into competitive" If you can do 3, you can do 10. Trust me, when you immerse yourself into the competitive nature of it, you won't want to stop. It usually takes a game or three at the start of the day for my hands to stop shaking -- but they do.
"I assume I suck and have gotten as good as I ever will be" NOPE. Nope nope nope nope. For one, if you play a lot of quickplay, you're going to get at least some modicum of mechanical skill, and mechanical skill can at least carry through bronze and silver by itself. If you have any game sense, you might just be past gold. And no, you haven't stopped getting better. For one thing, I understand being busy, what have you, work, but there's always *some* way to improve.
"so I feel bad for people that would be stuck with me on their team" never have this mindset. Matchmaking will put you with people whose skills you roughly belong with. It does seed from your quickplay performance. And also? The average player of this game really isn't all that good. You might feel like you're making a lot of stupid mistakes, but also? So is your teammate. So is your whole team. If you haven't played competitive, you are missing experience that's going to lead you to make mistakes, but also you'll be in a lower ELO where they cannot justifiably bitch out your mistakes because they're doing as bad if not worse.
" I guess I just assume everyone in competitive is much better than I am and I don’t want to drag anyone down with me" NOPE. Look, whether you're Grandmaster or Bronze quality, placement matches will put you where you belong. For example: I waited quite a while (til like level 123) to dip into competitive at all. I wanted stronger gamesense and knowledge of the characters. Now don't get me wrong, this did do me justice, and I ended up placing in Gold.... however, if I HAD done my placements earlier, I might have made Silver, or Bronze, because that would have been where I truly belonged. And then when I became the skill level that I am now, I would have grown to my current rank.
No, competitive is not too much for you. Matchmaking WILL put you where you belong one way or another, so you don't need to worry because you'll be the same skill as everyone else your rank, approximately.
But there's also no pressure to play competitive, if you just enjoy the fun gamemodes, maybe you don't need to try competitive. There's some toxic people but there's also some cheery and supportive people in competitive so don't be afraid to try it if you want to!