Whilst I agree with your points, I would never have wanted house price increases had I had the choice. That aspect is something that many have benefited from undeservedly and is a horrendous part of our society.
I don't know how you separate the people who have benefited from the undeserved increase in house prices vs the people who haven't. Perhaps wealth taxes? Windfall taxes? We are happy to do it on companies, why not individuals.
This, I'm fine with house prices not going up ridiculously.
The only advantage you can gain by this is moving from an expensive area to a non-expensive area if you are able to.
If you have to stay in the same area or own a house in a cheap area, house prices going up (as a homeowner) does not really benefit you at all.