As far as I understand the issue (and I am not a lawyer or involved in this kind of thing on either side), it would be the uploaders that would need sync licens

As far as I understand the issue (and I am not a lawyer or involved in this kind of thing on either side), it would be the uploaders that would need sync licenses, not YouTube, as YouTube is a hoster and the uploaders are ultimately responsible. If I understand correctly, YouTube's responsibility is based in the DMCA and is limited to taking things down and having some way of kicking off repeat infringers.