No, it is not terrible doing your day trips in reverse, ie Osaka to Kyoto. It is just a little less convenient since most folks tend to want more days in Kyoto than Osaka. You will just have a bit less flexibility for returning to the hotel for a nap, change of clothes or such during your touring in Kyoto and the evenings or early mornings are a bit less convenient. Trains do start early and run pretty late though. Either way, you are probably doing the best for yourself in selecting one or the other city and avoiding changing hotels during your stay in Kansai.

One other option I have found helpful when faced with hotel unavailability in Kyoto is to check for hotels in Nara. I have actually stayed there several times instead of Kyoto as the hotels tend to be rather more affordable and rarely sell out. This works best when you have a Japan Rail Pass but even without it the train cost is not bad for the short trip to/from Kyoto (under an hour.)