I know, you could do writes with Web 1, so it's imperfect, but since that imperfection carries on to Web 3, I kinda like it. In its "wrongness" it kinda suggests it's not that simple.
Web 3 might be "own" - but the -value- of what you own is questionable. There might be things of value in there, but if there is it's well hidden by the crap. "Web with blockchain" doesn't seem like a useful improvement over "Web without block chain" [1].
So I like your summary. It begs the question "own what?" Which in turn kinda answers the Web 3 question in a nutshell.
[1] apart from criminal activity, clearly the killer-app for crypto, the block-chain is useful for time-stamping things. It can be used to prove that say a piece of music existed at a specific point in time. Which could be useful in copyright questions. Granted, this is an astonishingly niche case though.