Is it possible to implement a "Travelling Salesman Calculator"?

Made specifically to plan out the shortest possible route between multiple cities using an in-built calculator akin to this:

It could become useful for some people…

Possible? Of course.

But not here. OSM at its heart is just a database, and there are many outside parties that build applications on top of it.

This would be another such application. Feel free.

I think several of the widely used OSM-based routers implement such a capability, see