Engine mounts, well the rubber bits anyway, do, over time degrade & both in the UK and here in New Zealand their condition is checked during an MoT or WoF inspection.
If the rubber is cracked or damaged then it's a fail & the mounting will need to be replaced. Now sometimes changing these mounts can be a long and arduous task...
Fortunately, for once at least, the mechanic Gods were looking down on me & this job turned out just about as 'easy' as it can get.
The basic principle is the same for many engine mounts, both for front & rear wheel cars. Things can get a whole lot more complicated if it's tucked away with limited access like the rear engine mount on the old Rav4 we stripped a year or so ago but you just apply a little common sense and things should work out.
Andy Mechanic