They do keep moving and switching arms to relieve stress and pressure on the muscles. After all, they’re actually not just there for fun - if you try to assault one and get past them, you’ll wind up dead / severely injured. Much as you’d expect with any guard with a weapon.
If they notice a build-up of crowd or disturbance, they stomp and switch hands a lot - that’s to get the people to notice they’re actually a loud, tough, stomping soldier, on guard duty.
If the stomping doesn’t work, they shout and / or have weapons ready.
They aren’t in a position to know who is or isn’t a real threat, or a disguised threat, so they treat any infraction on their ‘guard space’ as something too be countered.
Youtube Queen’s Guard for some fun videos of soldiers shouting, stomping, getting weapon-ready, posing for shots with kids, so on.
They are real soldiers, really guarding, and will take real action if required to protect what they’ve been told to guard.
They guard things like: the Crown Jewels (limitless value), Windsor Castle (see any other guards? Nope! They’re the front line), Buckingham Palace (same), Horseguard’s Parade (the clue is in the title).
A lot of tourists think it’s pomp and circumstance - and yes, the outfits are silly in today’s era. But they look nice, and they’re not slovenly unshaven khaki-dressed guards smoking and leaning on their post. They’re disciplined, functional, real soldiers, and as a few people have discovered, do not abide infraction on their role.
Even the idiot terrorists know not to go after them. Why on earth tourists mess with them I don’t know. Goading an armed soldier is never smart.
