Why do I need to completely desolder and clean the hole in the MB when I try to recap my board (Asus P4PA)?

The simplest way must be to simply "destroy" the old capacitors, keeping its leads on the motherboard and then solder the new capacitor on these leads?

Tell me why/why not to do this?

I have tried on another board (not an MB) to do this, and I found that it was possible to "pull" the old capacitor straight up and the leads would then slip out of the capacitor and left there (somewhat trimmed) to accomodate the new capacitor....