The arena has never been a realistic option to train girls, so why use it as the primary means?
1. You cannot train if you cannot win.
2. You cannot win if you use anything less than your best.
3. Even with your best, you still will lose roughly half the time (I'd say more than that). Once you get to your "proper" level, you start getting fights you usually can't win unless you improve, but you can't improve unless you get better equipment, buy up stats, or get a better girl. That costs money, and you get no money from fights you lose. (Of course, girl income is your main income, but fight income and troll income are valuable too.)
There are a lot of benefits to winning fights. Losing costs you mojo, but mojo is what you need to move up in the rankings and get the weekly bonuses.
Right now, opponent selection isn't very well done. Sometimes the fight is easy and sometimes it's hard. Sometimes the mojo payout is good and sometimes it is not (and you lose a lot if you lose the fight). And the two have nothing much to do with each other. You can sometimes have easy fights with big payouts, or hard fights with tiny payouts. (But a win is still a win.)
OTOH, what if you won mojo according to how difficult the fight was? Easy fights would pay less than hard fights. Also, opponent matching would not so frequently pair you with fights that are so very lopsided against you (there are very few matchups that you cannot tell for sure whether you'll win or lose).
Ideally, there would be NO penalty to lose a fight; this would allow you to always fight all opponents, regardless of your chances to win, because there's nothing to lose by losing the fight, and sometimes you might beat the tough opponent.
I do tend to use my Omega spot to train up a girl while I'm building up the cash for her, because the Omega girl never gets used. (She might get used if both players had really low Alpha and Beta girl stats, but that's just a guess.)