This isn't a good idea, in my opinion.
If you're playing a team VS team game, the only honors you should be concerned about is on your team. There's no point in honoring the opponent because the same honors apply to them as well. If they're honorable in any way, their teammates should be able to recognize that and honor accordingly. The opponent's vote isn't needed.
Riot could either leave you with two votes (1 for your team, 1 for the enemy team) or they could still leave you with one, making you choose between your own team and the enemy team. Either of these options are bad because the first one is almost implying that after you choose if you want to honor one of your teammates, you should also do that for the enemy team. The second option implies that if you don't spend that vote on your team, you can do so for the enemy team.
Why would you even care how the enemy team performed?
You should only be concerned about your own team's performance. And the categories we have now can't even be properly conveyed when we're talking about the enemy team as that requires communication and playing with them to know for sure. That's not something that's known to us, as their opponents and you should also not be concerned about establishing a good rapport with them in the all chat, in the middle of the game.