Is there any way to profit from PvP?

In the mobile version at least, MvM is an excellent way to make Bloonstones. The first attack per day earns you 5 stones, and subsequent attacks give you 3. There's also a 2 stone bonus for attacks you send that win (or are ignored by the enemy).

I rarely if ever defend against attacks, and it seems like a good 90%+ of other players ignore them as well. In the mobile version, there's no XP gain for winning, it's just cash, honor, and Bloontonium, which refills automatically. The only reason I care about honor is for achievements.

Cash win/loss wise, I've got so much cash that I don't even pay attention to it. My capacity is around 200k gold, and I have 1.8m. Aside from retrying boss fights, there's nothing to spend it on. I believe in general if I attack as often as my Bloontonium is full, I'll end up profiting.

Honor-wise, staying at low honor will probably end up pitting you against weaker opponents, although I think I generally gain honor by attacking as often as I can and losing every attack. Currently I'm at around 10k honor from this strategy. The losses are so slight compared to the gains that it's hard to stay low.