Living in the UK, I've experienced the Queen's Guard, or the Beefeaters, as we like to call them over here. I've never found them to be inefficient in any way: while they'll happily stand stoically as you take your photograph next to them, they'll also make sure anyone attempting to scale the gates or enter the grounds illegally are stopped in their tracks. I'm pretty sure there was a YouTube video where a Beefeater goes mental on someone who touches him? Anyway, as far as I've experience, they do their job well. Maybe lose the furry hats though, they must be a hindrance to agility and movement...
There have been a lot of stories about the queen's guard lashing out on tourists yes and getting angry with them. I honestly thought they were just there for show and entertainment. The tourists also mock and harass the guards. They're not taken seriously by the public and also tourists.
The Queen's Guard is a waste of time and resources, and the guards themselves are little more than dated symbolism. There is really no point to Queen's Guard, aside from aesthetics, which is a poor reason to keep them around. In all actuality, they seem to be little more than living monuments.
The Queen's Guard does not exist to be efficient. It is an obvious drain on funds and resources, but it continues in order to create a sense of stability and a prolonged sense of history and place within the English public. In many minds it is quite a bit outdated, but it gives a sense of comfort to the nostalgic and sentimental.