I was about to start a new thread but noticed this one.
So yes I totally agree with that proposal and I'd like to expand it a bit.
Besides what's suggested above, drag and drop box system instead of a queue we have no control of, for some people, me included, I think a simple change on the poke dex to reflect the boxes would help a lot. ie a border around each entry showing that you have that specific pokemon in your storage.
The caught function is okay, but I'd like to know if I have charizard's pre evolutions as well instead of just charizard that I evolved. Mostly for house keeping for the people wanting to have them all, for dex services and so on.
Also some naming tabs on the boxes or/and color coding them would be awesome.
A final change I'd like to see is a pokedex function to show you only the pokemon you're missing either as caught or from your boxes and also a separation by generation on the pokedex. Either in tabs or with a separator on the current listing.