When I set up the approval process for L4W (cribbing heavily from LEW's rules), I was primarily concerned with preventing attempts to cheat. As far as I can tell, that just doesn't happen. People don't seem to want to cheat at PbP. They make mistakes, yes, and having someone else go over your sheet to look for mistakes really is helpful, but I don't think it's nearly as important now as I thought it was back then.
In particular, I don't think it's very important to have all the mistakes fixed before starting an adventure. Yes, it's probably better to find out your +4 should be +3 before you start making attack rolls... but it's not game breaking if you swing a few times with the wrong bonuses.
So IMO if we think that the approval process is interfering with playing the game in some way, there's plenty of room to relax the process without risking disaster. On the other hand, it's not clear to me that the approval process is a problem for LEW. It seems like the (fairly few) people who submit characters get prompt responses -- at least compared to L4W, where we suck at this. If the process of actually filling out the character sheet is too hard... well, maybe. What could we do about that? Not clear to me.