The deterrent has worked though, nobody has dropped a nuke on people since the Americans in the 40's. Nobody having nukes would be a better idea of course, and save a lot of money all round, but it's not likely to happen anytime soon.
It does function though, the reason they do tests is to expand the envelope and identify faults. Or, do you think they're still testing the same things they were 5,10,20,40 years ago etc? The Vanguards were designed in the 70's and arrived in the 80's, they won't have been sailing around for 40 years not being able to work. We used to say in the RAF that our jets never worked (can't even remember if we were joking), and they were always having all sorts of faults in testing, but when they came to being needed they did their job exceptionally well.
Even the operators won't know much about what a test may be specifically testing, that's how the military works, basically just do what you're told, because someone above you was doing what they're told and so on. With a lot of secret things like this you have to go up a hell of a lot of levels before you get to someone who really knows what is going on, and why.
I wouldn't be surprised in the slightest if the tests they're doing now are more for the next class of submarines which are due in service in the early 30's. It's not like BAE are going to be allowed to sail a nuclear sub to the coast of the USA and start firing off missiles etc.
The press do a good job of getting the whole thing wrong, through lack of understanding and also through being intentionally misled, to me it's like one big act, until it's needed, then it gets fully proven etc.