It's not the desoldering...
When you find a machine which has been stricken by leaking capacitors or batteries, it's not the desoldering which leads to a world of pain. It's having to repair all the tracks and plated through holes on the PCB which have been dissolved by the leaking electrolyte.
Thankfully, most old kit has a PCB with only two layers - tracks on the top and bottom of the board, making repair possible if you know that you're doing. More modern kit, with four or more layers is a much, much more difficult repair. In fact, once you have buried layers, a repair may not even be possible.
The comment about RIFAs might be somewhat obscure for non-electronics nerds. It refers to a type of capacitor which is normally placed over the mains inputs to a power supply for noise suppression. Unfortunately, the plastic case of these particular capacitors develops cracks over time. These cracks allow moisture to seep in to the capacitor and once it has been damaged this way, can turn into a very smelly fire as soon as you plug the equipment in.