I would have found someone rubbing my back/touching me incredibly annoying.
And no I don't think that you're public property, and I am mystified by people whose partners think the day was mystical and magical - it was nice to meet her but she didn't do that much, the actual process of her being born wasn't transformative, we've had many much more awesome parenting days since.
However, when you say he won't be an advocate, what do you mean? Will he sit in the corner and play on his phone and ignore you? If he's asked a question will he shrug?
I did a course with my husband which was v useful and explained all the things that could happen, the choices we might have to make. And I did a v detailed birth plan, basically with alternatives - if A happens I'd like to do B, if B isn't possible please try C, only if there's no other choice do D, that kind of thing.
Some of the v helpful things my DH did was fetch a midwife when I needed pain relief and couldn't have moved myself, and answer/clarified some of the questions about A B and C when I couldn't.
I was clothed the whole time, medical staff examined me but despite forceps episiotomy 3rd degree tear etc once I had the epidural I was happily chatting away, before that I had quite poor care, a bad reaction to the induction and needed him to call people, and at one point basically to hold me up. It wasn't about him being a great advocate so much as someone else being there. And then when I had to have stiches he was with the baby.
Its unusual, but its your choice, I think the main thing I would be concerned about is you making it and regretting it. You would want him to be there immediately afterwards I think, largely because the chances of you being taken away from the baby aren't small, just for a little while. But the idea birth is a spectator sport is odd, and I don't know why that is many posters' focus.