I think you said some very insightful and interesting ideas in your post, even though I disagree with some of them. So first of all, (which you have probably have also already experienced), the strategies, especially in managing the economy, and overall the pace of the game, is very different in a best-of-13 rounds game than in a best-of-7 or 8 round games, and even though the specific tactics from round to round would look quite similar, buying expensive weapons like operators, and also ults would be more like "it's the last round, so use it or lose it" instead of trying to use it more strategically and save it for clutch moments or for rounds you must win. Shortening the number of rounds by half would also give people less of a chance to use the deep strategies and mind games that often come with longer games where both sides are trying to analyze and predict their opponents from the previous rounds in a game where aim and information and tactical positioning and equally important, thus making this deep game a lot more shallower, which could mean the difference between winning and losing in a higher level of play.
Part of the appeal of playing Valorant on a competitive level is this element of gameplay and the learning and adaptation, which cannot be adequately replicated in shorter, 20-minute games where every game is separated from every other one, so if the official competitive mode of the game is very different from the Premier or the VCT, then the gamers who are aiming to play in the tourmaments one day would not get the same experience in practice grinding for rank in regular competitive, and then having to switch over to the long-style best-of-13 rounds format for the more serious and professional games, which if this best of 7-8 competitive games are the only means of practice, it would severely hinder the performance of these aspiring pro players. Also, if Valorant did this, they might be seen by fans in a similar way as those scammy mobile ads which promise one thing in their promotions and advertisements, but deliver something completely different in the actual game, and people would call them out on their hipocrisy. Also, I know that a lot of these problems I stated earlier would be solved by simply including 2 ranked modes, one for the original best-or-13 rounds, and the other one being for the best of 7-8 rounds mode, and have the 2 ranks be separate, and I don't really see any issues with that other than possibly confusing fans, to give the busier or more casual fan also a way to experienced ranked gameplay, while not taking away from the more hardcore fans of this game.
Also when you brought up the fact that you think this game, as well as League, don't give your enough rewards for the time you spent playing them-I want to challenge that by saying that the purpose of playing games is for it to be fun, so if you feel like without the game giving you plenty of rewards you would feel like you are wasting your time, then maybe you should re-examine your reasons for picking up this game if the core gameplay and the experience itself isn't enough to make it fun for you. Although I know that factors outside of your control, such as AFK players, but the game makes sure that they do get punished, but the penalty of 20 unrated matches to get unbanned from ranked is a bit much, especially since disconnecting from a match happens to the best of us, whether it's from your internet service provider being inconsistent, or your game or even your computer crashes, and remember: that not everyone has the luxury of having fast reliable internet all of the time (and Riot just trying to make the best of the current situation while trying to provide a decent experience), having such a rule in place would likely have rippling negative profoundly-negative reactions affecting both Riot Games, as well as the whole playerbase, including you and me:
So first of all, the mandatory 20 games of unrated before being ranked-eligible again would discourage a lot of players from sticking with it and keep playing their game, since now they are doing something that they don't really want to do in order to get to the actual good parts of the game. The players not being there willingly could add to a lot of undesirable behaviors, such as flaming and blaming other players, intentionally throwing games, or even just going on autopilot and just sorta half-heartedly going through the motions to not get flagged as AFK (like how I did when I was trying to grind to level 20 within a short period of time), or even just 5-stack with their friends and just surrender matches early to save on time, and this sort of behavior would directly clash with the people actually want to play unrated for fun, or actually care about winning. The last thing a game developer wants is for their game to feel like a burden and a drag. The separation between unrated and competitive exists for a reason, and that is to put like-minded players, whether casual or tryhard, together to make it more fair and fun for all players, and having such a rule would directly go against this goal, and I think the current comp bans and RR reduction would be enough to discourage players from going AFK in competitive games, without going too overboard.
Also if your current life situation simply doesn't allow you to set aside 40-minute blocks of time to commit and mentally-focus on winning one game with the same people on the same map, then I hate to break it to you- but this style of gaming might not fit the best with your lifestyle currently. Look: I am not one of those sexist people who believe that women should be raising their kids instead of playing fps games, and that gaming, in moderation is a good way to unwind and de-stress after a long hard day, but if the current format for Valorant competitive is not working for you, there are plenty of other games out there that can better fit your thirst for competition, taste, and session time requirements, if this is such an issue for you. (Like for me I'm not gonna be playing in the upcoming premier because school is starting, and I can no longer sets aside 1-2 hours a week for Valorant during the weekday, it just doesn't fit with my lifestyle anymore and I'm okay with it.) I'm not telling you to give up Valorant, but just check out the options out there if you haven't already.
Also about the skin market idea I really think that in the way you're describing it it is very doable, and it can really be a boon for the community, while still remaining quite profitable for Riot Games. It does take a bit of power from their hands, and adds some more unpredictability to the skins economy, and if the company really wants to make it work, they probably could like CS:GO did, but you got to remember-the culture within these 2 games are very different, with CS:GO giving players more control and agency to create their own maps and gamemodes (similar to Roblox), and also truly "own" their skins, in the sense that they can buy and sell them on the market as they wished, while Valorant wants to be the sole decider of how their game should be played, as well as the sole vendor for their gun skin, so I guess it's really just a company choice. The same goes for how much they want to sell their skins for, but at least this game is still free-to-play, and you don't have to actually buy any if you can't afford it or just don't want to (I don't own any skins myself either.)
(Also note to Mike: I know that this is 6 paragraphs long rather than 5, but I need this length to address all the points OP made in her very long post. Please don't take any action against my account.)