The Issue:
Alot of us pvpers who catch our own pokemon are perfectionists and for most of us that means a full pokemon inventory all the time and hours after hours of hunting if not days.
The Solution:
What I'm suggesting is no new feature to the game but an improvement on the old feature, by this I basically mean a way of viewing caught pokemon even while your inventory is full, as in every caught pokemon becomes displayed before being sent to your PC. This could only apply for caught pokemon or all gained pokemons for that matter.