If the stage doesn't quantifiably interact with the scoreboard outside of the context of player vs. player, by definition the use of stage to one's advantage has to exist solely within the context of PVP play. I'm a fan of a conservative stagelist by value criterion of player vs. player, but even I realize that if logically followed the Japanese ruleset and stagelist LIMITS player vs. player, not enhances it.
Aka, you can't gain an advantage from FD over your opponent if you don't know how to use it. You can't gain an advantage over Delfino if you don't know how to use it. You can't win on the most neutral of stages if you don't know how to use it. It's hypocritical for someone to claim "play me on 'neutrals', stop playing 'bad characters', and 'get better'" when in fact the increased depth by definition would require a larger and more versatile skill set (including adaptability god forbid) than simply playing on a single or limited stages.
TLDR: Play on whatever stages are competitively sound, stop playing characters that can only handle static stages thus making them "bad" or pick up another character that can fully maximize usage on a specific stage thus increasing your overall skill, and get better and stop blaming your shortcomings as a player with your inability to adapt and utilize tools on an appeal to player vs. player.
On the note of Melee, it's intellectually dishonest to claim that the ruleset of commons appealing over time to a smaller list is due to wanting increased player vs. player interaction. It's more likely the result of the "starter stages" being commonly universal throughout the country. Since specific counterpicks occurred as regional quirks, they were less likely to receive widespread use thus less likely to retain their common usage over time. The loss of depth isn't so much an appeal towards player vs. player as it is commentary towards the negatives of dividing stages in terms of starter/counterpick ideologically.