I think this issue is one that arises more in IV, as you say - it's easy to get enough attendance in II and III to have plenty of cash for your arena, but the money in IV is very very tight.
i don't see much of a difference between income from division III and division IV. at least i'd say you make about the same (or slightly more) by having a winning season on div IV than having a bumpy season on div III.
not only in terms of arena btw. you can get less merchandise income in div III than on div IV depending on your winning record. the only real difference is tv money, but it's not a huge impactful difference.