Are hotel reservations a *must* in Loire in September?

Would you make the choice in the morning or day before and then reserve online or by phone? I assume you'd want some confirmation before starting the bike journey. With a car, I'd have less concern; have not done any biking myself. Traveling flexibly is easier if your requirements and budget are also flexible.

I think what we'd really like to do is arrive somewhere in the early to mid-afternoon and say to ourselves, "Let's find a place near here for tonight..." Is that at all reasonable in September (after high season)?

I am terrible at finding hotels last minute and super at finding them in advance. We always pay too much and spend way to much time searching when we do it on the fly. What does work is to have the clerk at today's hotel call ahead to book you for the next day. If you start with hotels you want to use you can at least call ahead a little to book. (I once had a list of 6 nice hotels and none was available as we drove around worrying that we would have no place to sleep; we finally ended up at a terrible chain with a concrete platform for a bed with a foam mattress on it. The bed was poured into the floor) The problem with arriving in a town and then looking is that your time is so much better spent enjoying the town than beating the bushes for a place to lay your head.