In American society, I believe that poetry has little influence beyond the people who write and read it. I am not sure about present day Russia but poets have been treated as stars there in the past. Huge crowds would turn out to hear prominent poets there. In some Latin countries poets still are revered by large portions of the population.
I attended a reading here in Eugene,Oregon last year and there were more than 300 people to hear W. S. Merwin, and there are other poets like Billy Collins that draw a lot of people, but poetry just does not influence this society that much.