The little plates they stand on

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Those nice shoes are probably too big of an expense for the governments pitiful economy to keep replacing. The plates keep the bottom of the shoes from wearing out.

The shoes have metal soles in them, and that plate is an electromagnet that keeps the traffic girl from escaping.

Or it's an electroplate that shocks them if they screw up.

I thought of a new possibility - the plates are there to keep the street from wearing out. With all that constant turning, over time a hole would eventually wear into the pavement, and the traffic girl would end up standing in a hole.

I agree with Member Jong - if you look around the plate the street is worn. It is probably also easier to turn on the plate as it appears more smooth than the surronding pavement. Maybe the DPRK is more inovative than we give credit!

Also, their pavement is probably poor quality and would wear out quicker.

In all seriousness, watch one of the videos and think about how many turns they do a minute - in an hour - in a day - over the course of a year. There would be considerable wear on the shoes and the street. And the plates do make for smoother spins.
The plates are an improvement trifecta - shoes, street and motion.