You know the saying "If it ain't broke, don't fix it", right? You need to prove the current system is broken first. ]You've discussed it, but you haven't really explained why or how it is flawed, in all honesty.
Which brings us back here. I'll try to sit down and do this again but go into extreme detail to hopefully not miss anything and help it be clearer, let me know where I can clarify anything.
Currently, we have certain types of stages as starter stages and others as counterpick stages.
Game one is the most important game in an entire set as the winner has the most control in terms of counterpicking stages, it's a serious advantage. In theory this means the first match should be played on as equal ground as possible to ensure the system is as fair as possible for most players. The problem is it isn't.
Currently, starter stages are general stages with no special effects of any kind and are flat with possibly a few platforms of varying number and positions. This favors characters stronger on "flat/plat" stages. (This is the meta we currently live in where they are stronger, it is of our own creation.) Let's look at characters that have more adaptability and can function in other kinds of stages and stages with special effects, movement, or any other gimick better. They are put at a disadvantage by having these as the stage they must play on first as the most important game.
Now, this could easily be argued against as "this is the meta, some characters will be good and others wont" but there is another problem: this style of stage selection gives ANOTHER advantage to those flat/plat characters.
We'll look at two scenarios. With stage striking, the flat/plat character get's a flat/plat stage since those are the only ones available (HUGE advantage getting one of your top 5 best stages if we're looking at Brawl right?). Let's say the flat/plat character won the first round. Now, the more adaptable character picks a counterpick stage to help them boost that adaptable quality they have, thus beating the flat/plat character (which there are VERY few of now a days since most just get banned even if they are perfectly good for play as I've pointed out in too many threads by TOs just because they don't personally like them and/or get beaten on them making this even more of a disadvantage). So game three comes along! Even with a ban, a flat plat character can go to optimally their 2nd best stage for game 3 and is likely to do so giving them an INSANE advantage that shuts down a lot of characters.
Now maybe that adaptable character manages to snag game one by luck. The flat/plat character can easily go to any flat/plat they want, there is NO way that banning the stages can effect this, there are so many legal. They WILL get at a minimum their second best stage for the second match, while the adaptable character may be stuck with anywhere from their 3rd to 4th best stage if they were in this position.
In short, just like in having an all FD ruleset our current ruleset favors heavily a certain type of character with a huge bias and is no better then an FD only ruleset in that manner.
The better solution comes in striking from a full list of legal stages. This allows for the most neutral stage possible for match one and keeps match one as fair as possible eliminating many of these issues. When I say neutral, I mean the stage closest to their actual matchup ratio, a stage that favors neither in a hugely significant way.
For this to work you need to have a decent number of stages, and the best part is certain stages that can't be legal because a few characters can exploit them in some way CAN be legal for all of the matchups it doesn't effect, as players can strike those stages in the relevant matchups. This allows not only for more variety, but a fairer ruleset as well.