Browser vendor/version is hugely important information for triaging issues and implementing progressive enhancement approaches on large scale websites.
Edit: OK, this isn't progressive enhancement. But it's still a major problem you have to sniff the User-Agent for. I don't want to sniff UAs either but when Chrome is wont to change how fundamental parts of the web work like cookies it's sometimes necessary. I know UA hints will still allow you to do this, but requiring a second request is going to make things like redirect pages difficult to implement.
The "main advantages" section for client hints all seem to apply there.
UA hints solve nothing, even after reading the spec