I really don't care if people "support" various forms of extreme violence by watching youtube movies. That is WAY better than supporting it by committing various forms of extreme violence.

Is there any actual evidence that these youtube videos are in fact driving people to commit acts of terrorism?

yes https://www.ncbi.nlm.nih.gov/pmc/articles/PMC300808/

Why then are they posted?

In hope they'll make people become terrorists. That is not the same as observing those videos actually do it.

Also, some of them are probably posted just so that the Western media can find them and scare the population shitless with them, pumping the huge autoimmune response we have wrt. terrorism here.

If cable companies are monopolies, surely Google is as well.