Why do dance rhythms seem to...

show up so often in the music of so many famous Russian composers?

Mussorgsky, Shostakovich, Tchaikovsky, Shchedrin, Prokofiev, Kabalevsky- the list goes on and on.

It just seems like Russian composers have incorporated folk music and dance rhythms in their work more often than composers of other nationalities. Why is this? (I can already see that this is a dangerous generalization, but I'm curious.)

Nationalism, combined with a knowledge of exoticism in the traveling composers' cases.

Why would anyone use folk music as a starting point?

A lot of it has to do with Nationalism.