No, it is the other way around. The website decides if your software stack is allowed to view them.
1. Windows to old? Blocked.
2. Running FreeBSD? Blocked.
3. Patched your version of Chrome? Nope.
4. Your Linux distribution isn't approved? Blocked.
5. You want to use some obscure Chromium derivative? Absolutely not.
6. Running a RISC-V machine? LOL get lost.
Basically the user-agent is no longer the agent of the user. Instead the website can select which hardware and software stack can be used to access the website.
The inevitable outcome is that a huge number of sites will only allow OSes from Microsoft, Apple and Google running official browsers by the same three megacorps. Everything else will be blocked.