Compromise is often a good idea. However, the idea we should have half as many Trident submarines is likely to please noone.
The fundamental problem with Trident is, when can you morally use it? It is hard to see the circumstances under which a sane British Prime Minister would liquidate a million or so people, which means it is really for saber rattling, which means an intelligent foreign power can probably guess we wouldn’t use it.
The thinking around its independence is also a muddle. While we are aligned, to some extent, with the United States, we are never going to fire Trident against their wishes. So its not independent. If we become decoupled from the United States, they can simply refuse to service the system and within a year its useless (and that is if you believe the government that the US has no power to stop it being fired. Would you sell someone nuclear weapons without a secret off switch?)