Wheeled luggage is much better for navigating train stations and trains, with the exception of your Koyasan trip.
You will find it difficult to haul large luggage along the route to Koyasan. So, when you leave Kyoto, take a small overnight bag (and a small overnight size backpack is a great idea for this section of your travel) and ship your luggage to your Osaka hotel.
The route to Koyasan involves several transfers, a very steep cable car ride, and a bus where you get on and off with your luggage. The less you are carrying, the better you will feel at the end!