I agree. I personally think the fleece lining is much easier to clean, more cost effective in the long run and safer for chinchillas than most bedding's. Your local craft store will often have sales on fabrics and that would be the best time to go and get a couple yards, depending on how big/small your cage is. Plus, it makes the cage look super nice and cute depending on what fabrics you choose. If you end up with left over fabrics you can also make your Chinchilla a nice hammock or something!
With the fleece I just sweep up the poops with a tiny dust pan I got at the dollar store once a day. Chinchillas are super low odor, so I imagine washing the fleece liners once a week or every other week would be just fine. Weather you decide fleece liners/aspen/kiln dried pine/, just keep away from kitty litter, ceder, newspaper, for sure. There is controversy on the kiln dried pine though as it can cause respiratory problems if it was not treated properly.