Try as I might, I just can't bring myself to care about how a player goes about creating a character.
Swimming upthread a bit for this quote, but, this, right here, is the heart of the issue AFAIC. Min/maxxing or powergaming or whatever, is an issue when someone else makes it an issue. Very few people would describe their choices as min/maxxing. And, with 30 seconds, you can justify pretty much any character building decision you care to choose. The issue here is that there are players, primarily DM's, who feel that it is incumbent upon themselves to police the players and make sure that those players are playing "right".
While the persistent mantra is "trust your DM", I find that the opposite "trust your players", while equally true, is practiced a lot less frequently.
I only reward inspiration when putting yourself into a disadvantage by playing out a flaw, which is what min-maxers usually don't do. They would just complain "What's the point of inspiration when you first have to get disadvantage to even get it?" sometimes, but usually they just accept my rule silently. While my players that are heavily into roleplaying just play out their flaws anyway and are more like "Heh, I didn't actually do this to get inspiration, I just wanted to play out my character, but nice."
To me, this is a case in point. Note that [MENTION=6801585]Rya.Reisender[/MENTION] has adjusted the mechanics for Inpiration. This isn't what is in the PHB. The question I ask is, "why?" Why alter the rules? You want to encourage players to play up their flaws, but, only their flaws? Doesn't that mean that players will become just a collection of flaws, rather than presenting well rounded individuals? Sure, characters have flaws and those should certainly inform play, fair enough. But, that's just one facet of a character. There are also goals and beliefs too, if we're sticking with just the stuff from Backgrounds. Why are those not also given equal weight and rewarded equally?
Look, it's your game, and do what makes you happy. But, for me, I think that this approach may not produce the best results.