No, I wouldn't feel "stacked on top of each other" if I were a multi-millionaire in Paris.
But, in the real world, your talking about putting families into 600sqft (at very best) boxes, with audible neighbors on every side of the unit, and no way to go anywhere (no parking, no meaningful transport, because 'everything we'd let you have is a short walk away')
If you actually do what you've described, and give everyone their own townhouse, you've just reinvented the modern suburb. Because that's what modern suburbs look like, everyone in a townhouse, or a townhouse with some small strips of yard around it.
> but there are many different ways to live in a dense city
Sure, but only if you are fantastically wealthy.