Some thoughts...
September is a busy month on this route. I would reserve your first night or two, just to give yourself peace of mind, and then make a decision about whether or not to reserve - after you assess the amount of traffic on the trail and in the places you have selected to stay.
In October some places are beginning to close.
Another factor is whether the number of walkers declines after Conques. You will get a sense of that as you walk.
As you get a sense of how far you will probably walk each day, you can check your guidebook (most people carry Miam Miam Dodo) and see how many lodging options are available and how many beds they offer.
Places that offer dinner like to know, in advance, the count they will need to serve. This may be the best reason to reserve.
And, yes, I also prefer not to reserve ahead. But I have done it on this route.
Bon chemin!
Tom