Boviously, the answer is the same as everything else in climbing: it depends.
Freeing a stuck rope could expose you to bad weather. It could lead to sketchy poorly-protected or unprotected climbing. It could prove impossible and leave you with much less rope. It could be a huge problem.
Another way to avoid rapping off the end of the rope might be to very carefully watch the end of the rope while you're rappelling.
An option for rapping not mentioned yet is to tie knots in the ends, then stuff it into a sack and rap with the sack. Good for windy conditions, rope-eating flakes, and not-vertical terrain.