What I don't understand is, why can't we just have a browser that doesn't give any of those details that is used to determine unique a browser. It doesn't make sense to allow a website to have access to that info.
You mean like the tor-browser? It's not that they don't exist it's more that they're pointless if they're not used by lots of people.
Personally I'm more in favour of randomizing some of the properties. That way you don't need to rely on being unique. In the end it's all about how much information you're transmitting about your identity, and while picking a common value is one way of increasing entropy picking a random value is much more effective.
You don't actually want that. Not giving up those details is information unto itself. You want a browser that gives up the same bits as everyone else's browsers so they can't tell it apart from the others.