I think they’re allowed to do that to relieve muscle stress. It’s a difficult job, but part of the point is that our volunteer citizen army doesn’t threaten the public unless there is a credible danger. I often visit Warminster - which has the School of Infantry attached - and nobody takes any notice of the soldiers wandering around in large numbers. We are neither frightened of them nor do we venerate them.
Having said that, there are regiments you probably wouldn’t want on guard duty at the palaces or government buildings. I suspect if it was the Paras or the Hereford lot and a tourist tried something on there would be no reaction at the time - but he might get a nasty surprise later*. Which is why it tends to be the really respectable formations, like the Guards and, nowadays, the Royal Marines.
*These are the people who would have several observers in the crowd for every one on actual duty, because they’re like that.
