The fleece doesn't cover the whole cage, it stops about two inches from the bottom. The cage is only covered at night, in hopes that she may get used to sleeping at night and being active during the day.
This is probably not a good idea. Hedgehogs are naturally nocturnal animals, and to mess up their natural cycles of sleeping and waking can be harmful. Even if it weren't, putting a blanket over the cage would be a little counter intuitive - making it dark would encourage them to be awake, and vice-verse. It's recommended that you have a consistent light schedule to encourage their circadian rhythm so that they are provided with around 12-14 hours of light during the day and 10-12 hours of darkness during the night.
Fleece liners are also probably the best way to go. I haven't used anything else so I can't talk about the good side of all the other options out there (though I doubt there are many unless you are a breeder with expectant mothers), but I can say that I've washed liners in both the washer machine and in the sink by hand and it really isn't that gross. You can always do an extra rinse cycle in between hedgie loads and people loads (: