* Damaging the oil pan: Forced maneuvering can bend or crack the pan.
* Stripping bolts: A lack of space makes it easier to cross-thread or strip bolts.
* Damaging surrounding components: The engine might be in a position where you risk hitting or scratching other parts.
The small amount of extra time spent loosening the engine mounts is far outweighed by the reduced risk of damage and frustration. It's a much easier job with a bit more room to work.