Hunger is manageable as long as you eat up to full before you leave to do stuff. To top off, you can either rest to make room for more meat, or just eat a frozen pizza for the last bit. Other, more costly solutions include eating at the gym or the pizza place, saving time it would take to go home.
There are various tweaks I would suggest to the game balance.
For one, it would make sense for your non-combat Energy bar to effect your combat Energy in a way similar to how Health works inside/outside of combat. This would make the game slightly harder, so some mild buff might be in order to compensate, but it would need to be very minor.
I'm not sure if food and happiness should affect combat, but it would be worth tinkering with.
Health damage doesn't seem to stick that hard. It's pretty rare that I'm waiting on my Health rather than something else. Realistically, you shouldn't be able to train or start fights below 20% health at all, and you should be penalized for training somewhere around 50 or 75% or so. But again, this kind of change would call for a sweeping rebalance to compensate as well. Losing fights should be a moderate setback, and more so for the unscrupulous Ultimate fights.
I think stat point training should be buffered, lagging by about one day. There could be a grey bar for ongoing progress that gradually turns solid over time, and similarly, the stat drain per day could also be continuous. The point being that if I'm almost at 9 strength, I shouldn't be able to do 10 reps and then suddenly have 9 strength for a fight later in the day. If anything, I should be sore.
I've found the end-of-day interruptions to be a bit tiresome. The only thing that should actually interrupt you is when you absolutely must go to a fight you signed up for.