I know rules wise you aren't allowed to give each other/bribe each other power tokens, but I think that's really lame.

Do you think it'd be ok if players were allowed to give each other power tokens? I wonder for what balance reason is it that power tokens are so explicitly separated by house in this game?

The balance reason is that other players can't stop, alter, or prevent these kind of deals, and power is used for so much else that it's extremely important. Power is also an abstract representation of political, economic, and military strength for that House, and that house alone within its sphere of influence. There are already other mechanics to represent more direct military support in the Support and Raids. What's more, direct trade of power allows two players who are on opposite sides of the map to make deals, which should be discouraged since it allows two players who don't have to worry about each others' borders to team up in an effective way. Meanwhile, players who make deals with neighbors have to constantly worry whether that person will abandon, or attack them at a moment of weakness, but in turn, they can get direct and powerful support and raids used to help.

If you really want to trade power, make a deal where you say you'll place an Consolidate power order in an area next to another player, and he'll play a Raid in that adjacent area. It's simple, effective, and allowed within the rules, so long as you don't show which order you are actually placing down.

This balances things out things, and makes it so that it's a move that can be disrupted by good play from other players, or leaves you open to treachery from your supposed ally.