You are running on 2 assumptions.
1.) GCC doesn't understand the risk when it offers its base to the US.
2.) Iran will "win" by playing a long game.
Well, GCC knows the risk when they offered their base to the US, it's not like "Oh, we don't know basingthe US fleet here in Bahrain will make someone attack us" Unless either all those GCC administrators are extremely incompetent, they know the risk involved, the issue here is why they ask the US to base their naval and air fleet in their country in the first place. That's already shown during the first Gulf War forward, when Jordanian land was attacked, and their pilot was actually and literally burned alive. The key is geopolitical cooperation. I can write an entire article on this, but I will just be short here. They needed the US presence in the region. Because of the trade route, until China or someone else can guarantee the security at sea, they will need the Ameircan present. And China is not interested in becoming the world Police.
Second point being, nobody would win, not Israel, not the US, and definitely not Iran, if we are playing the long game. First of all, what is winning? If by US win is an Iranian regime change, that may or may not happen, not holding my hopes up, if by Israel win, that means a destruction of Iran, then that's NOT going to happen. And if Iran wins, it's a destruction of Israel, that's not going to happen, or pushing the US out of the region? Well, that's not really up to them now, is it, and as long as Isreal exist, it's not going to happen, even if we are talking about remaining as it is, minding its own business, how's that a win for Iran?
Now the question is, what would Iran do? Hence, the dilemma I suggested. You want to keep attacking the US and Israel assets? If that is the way you try to go punch on punch, Iran is not going to get anywhere because they can't touch the US, even if you can neutralise Israel, US weapons in the region are just one month away. And trust me when I say it, with 11 aircraft carriers, sending a pair each, you can have 4 to 5 rotations that last a lot longer than 1 month. How about attacking other GCC nations and spreading it equally? Well, you may send fear to the GCC, and they stop supporting the US. Well, sure, never say never, but you have an equally, if not a better chance, to further piss off the GCC nation by bombing their country.