Part of that is the result of easier distribution, cheaper production, and more available leasure for classes able to do creation.
How the copyright system influence this is (to my mind) uncertain. The system may be positive, or it may be negative. There isn't sufficient research nor natural experiments to know. I strongly suspect some level of copyright protection is positive, but there are too many variables to be able to be certain.
While I wouldn't be surprised if most people in the UK don't want the filters, this data by itself is not really representative.
I presume most households already have Internet. New customers will to a large degree be people that are moving out on their own, and young adults living by themselves are less likely to want a porn filter than somebody with children. (And people with children are less likely to have available time to rurn things on.)
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.
How the copyright system influence this is (to my mind) uncertain. The system may be positive, or it may be negative. There isn't sufficient research nor natural experiments to know. I strongly suspect some level of copyright protection is positive, but there are too many variables to be able to be certain.