In pokemon games what is the point of all the different boxes in Bill's pc?

The PC is mainly used for Pokemon Storage. You can only have up to 6 pokemon in your team. Anymore pokemon you catch will be sent to the PC. There, you can withdraw or deposit your pokemon.

Well the point is to not run out of room for Pokemon. They don't want you to want to catch more Pokemon but be told you don't have any more room. If you wanted you could delete Pokemon you don't particularly care for, but that would be really hard for me personally, just cause I'm a sap like that. As for the second question, I don't really know what you're asking, but I think it's something like trading to a new generation with high level Pokemon so you can beat the game faster. If so, I don't personally do that. I prefer to start from the beginning and work my way up. Of course I'll trade any Pokemon I want to my new game, but I won't use them to get through the game faster.

The PC is there for anyone who wants to actually attempt to cath 'em all. Or if you want to keep more then 26 pokemon in Yellow, you need to use the other boxes. I know the Bill's storage system is quite bad in the first 2 games but from Gen 3 onwards, it has a dramatic improvement. If you don't care about getting different kinds of pokemon, then you can release the lower level ones. And no, I don't trade pokemon to help me in the game. This is mainly because I have no friends to trade with and I don't have extra consoles.

The boxes are for storage, some people do what you're suppose to and catches them all. And, no, transfer from gba game to ds game requires the elite four to be beaten on the ds game, games on the same system require two systems, which most people don't have.

yThe point of the pokemon games beening to catch them all in every gen the box total cap is the total number of pokemon revealed in the game 4th gen was 493 so you have room to keep every pokemon in the game

Yes, some people do switch stronger pokemon to a newer save file on a different game so they can get through quicker. Personally I trade my starting pokemon over, train him/her up, then trade it back.

i organize my pokemon by type so each box has a different type

The PC is there for anyone who wants to actually attempt to cath 'em all. Or if you want to keep more then 26 pokemon in Yellow, you need to use the other boxes. I know the Bill's storage system is quite bad in the first 2 games but from Gen 3 onwards, it has a dramatic improvement. If you don't care about getting different kinds of pokemon, then you can release the lower level ones. And no, I don't trade pokemon to help me in the game. This is mainly because I have no friends to trade with and I don't have extra consoles.

Well the point is to not run out of room for Pokemon. They don't want you to want to catch more Pokemon but be told you don't have any more room. If you wanted you could delete Pokemon you don't particularly care for, but that would be really hard for me personally, just cause I'm a sap like that. As for the second question, I don't really know what you're asking, but I think it's something like trading to a new generation with high level Pokemon so you can beat the game faster. If so, I don't personally do that. I prefer to start from the beginning and work my way up. Of course I'll trade any Pokemon I want to my new game, but I won't use them to get through the game faster.