Though if you're doing a "speed run", getting items that you can't quite immediately use might not be that bad. Speed runs are supposed to be a challenge. If you have extra low stats because you skipped every optional quest, being further penalized (by not being able to use the super high end equipment) is probably okay.
I'd say, make sure that people who are somewhat casually going through the game (who do some sidequests, leveling up, who therefore have higher stats) can equip everything they find.
Equipment essential for the completion of quests being the exception, of course.
Are you planing on letting people use the mall throughout their whole run? If so, at the end of a run, a player can just "sell" everything they have to a multi, and then "sell" it back at the very start of the next run. (And by "sell" I mean, "give for some nominal fee".)
