I don't know if this is helpful, but I'm a relatively new player and I've had a great deal of interest in competitive, but have yet to jump in. Here are a couple of my thoughts, sorry for the ramble:

(1) I'm really nervous to get into scrims or pugs, even the newbie ones, when I have almost no contact with the format. I play a good deal of 5CP in casual, but even without any real experience in 6s, I know that 5CP in casual is not a substitute for 5CP in 6s. On occasion, you can find a game that feels fairly balanced and is 7v7 or 8v8 or something in casual and it has been some of the most fun I've had in TF2 so far. If there was a no-restrictions (or restricted, either or) 6s matchmaking system that was (1) used frequently and (2) not horrifically broken, I think it would help me and other new players build confidence to get involved further.

(2) Someone mentioned it already, but the system for getting involved feels confusing and a bit daunting. I think this one is probably trickier to solve, especially since there is no in-game competitive gamemode [Competitive Mode Matchmaking, y'know?] that people use. But in my experience, I've had trouble figuring where I can play pugs of 6s as a noob without being greatly outside of my skill level.

(3) Skill reccs./culture of improvement. "Culture of improvement" is sort of a stand in phrase, because it doesn't really capture what I'm trying to get at. Maybe it's seriousness. I really want to play 6s, and I want to improve to some degree at the game. But I'm an older guy who has to take time for family and work, so what improvement looks like for someone similarly situated is going to be lower than someone with more time to dedicate. Again, I don't have much experience, I just play/watch/read about TF2 quite a bit, but it doesn't feel like there's much of a space for people in my position. I don't know, I'm having a hard time getting across my sentiment here. I guess I just want to play games of 6s where people take it seriously enough to not deliberately throw, but still be relaxed enough to laugh when things hit the fan and stay positive in a loss.
It would also be really helpful to have a regularly updated guide (either written or audiovisual) on what skills you should have before getting involved in competitive. I did a couple scrims during the last (i think) newbie cup and I didn't feel completely out of my depth, but I did feel like I was noticeably outskilled in these matches. I'm guessing this is just a difficulty with a smaller playerbase in a game that has such a crazy skill ceiling, but I've run into plenty of people on casual who have expressed interest in competitive/the 6s format who've cited similar worries as their reason for staying in casual/community servers.

(4) "Edutainment" YT videos on 6s. This is only loosely related to my experiences as a TF2 noob who's interested in 6s, but what gets me interested in a game's competitive scene is either playing the game or seeing someone on YT who can break down what is cool about the game's competitive format in a digestible way. I think there's a lot of room for "breakdowns" of interesting matches that gives newcomers a greater understanding of the format and it's nuances. The closest analogue I can think of is the YT channel "Ocie". They do breakdowns of Overwatch matches in various skill divisions, explaining how advantages, disadvantages, etc. affect individual matches. I don't really like the general feel of Overwatch as a game, but I've gained a lot of respect for the competitive scene in that game because Ocie's videos have given me some understanding of what is happening in game and why.

Sorry if this is a bit scattered, just trying to get some of these thoughts out