The different transactions change the block hash, though, so it's the same problem for the attacker that you originally pointed out with proof-of-work, no?
The problem is that you've introduced trust into a trust-free system. And you didn't even pick wisely, you picked wealthy.
The assumption used to justify wealthy is that people that are wealthy will want to preserve the system, and it's value. They are actually more likely driven with increasing their wealth.
This, of course, is not unreasonable. But a "pretty cracked up currency" is still okay to enough people. You can't trust people to judge the crackedupness of a (psuedonymous) system. This is the same reason "regular banking" fails.
@David, this would probably cause some trouble amongst those wealthy people.