Some quick research shows that a big part of the problem is diet: squirrels require a surprisingly complex and varied diet that is hard for pet owners to replicate. Getting them enough physical activity is also an issue.
(Of course, one might suspect that it would be cruel to keep squirrels in such unnatural conditions, but the same could be said of most pets.)
[edit: Apparently keeping wild, undomesticated squirrels as pets was popular at one point (https://www.atlasobscura.com/articles/pet-squirrel-craze ). That article doesn't say why the trend died out, other than...all of the obvious reasons.]
[edit 2: Would a squirrel raised indoors always think it was summer, or would they start storing and then digging up food as the year progressed even with no change in temperature? Might be relevant.]