I agree that it is frustrating and something must be done. I'm not sure that the highest rank per day is best, as it's pretty easy to win #1 at some point during off-hours, especially if no one is defending.
In the absence of some sort of MMR system, I'd suggest that everyone's Arena payout is set randomly between 15 minutes before and after the payout time (different for each person, and changes each day). There will still be people defending (and you may not be able to get your #1 spot each day because of it), but you won't have the problem with people basically locking up #1 from 10+ minutes prior to payout each day.
