I'm beginning to think the reason Monarchs don't walk and live amongst their people is to protect them for the frightening side of casual power. To keep them from overstepping their bounds or even being tempted to do so.
A Monarch coming down to walk the same filth ridden streets a peasant walks, with their own two feet no less, such a thought is frightening for the local rulers, exciting for the people and an unknown experience for the Monarch.
The local rulers of such a filthy place will no doubt want to hide said filth from the peering eyes of the Monarch, to now have them walk through it, it's as though they should go ahead and hang themselves. And for the people they will be excited, the Monarch is a mystery usually and far off to their problems, the closest they can get is the local rulers and those aren't often what they need.