Why doesnt the cursor go into the search bar on youtube?

Best guess:

Whoever coded YouTube’s main page did not set it to steal focus.

That’s exactly it. Web designers have the ability to put the cursor in any text form element, which is what that search bar is. Search engines do it because obviously people come to their site to search, so it saves effort. YouTube’s designer hasn’t implemented the cursor move, likely due to them wanting people to view their main page, since they feature videos there.