You're technically not allowed to download YouTube videos anyway, there just isn't a convenient measure against it. You're not paying, you're probably blocking ads and now you want to download stuff for free? You're worthless to creators.
Also, you're not getting to see all the videos that aren't on Youtube exactly because there is no DRM.
No, because DRM + DMCA has repeatedly been used to violate consumers' and researchers' fair use rights. It's my right to lock my house, unless you're inside it and I'm effectively turning it into a prison.
If I buy a movie on Google Play Movies, I have the right to make up to 7 backups without DRM, but DRM prevents me from that.
Absolutely. That's not particularly relevant to the normative question of whether the HTML standard should make adding DRM less of a pain point though.
No, they have no right to control my computer