Absolutely, yes! A protocol should not be tied to client details. Where did "User Agent" strings even come from?
They're in the HTTP/1.0 spec. https://www.rfc-editor.org/rfc/rfc1945#section-10.15
10.15 User-Agent
The User-Agent request-header field contains information about the
user agent originating the request. This is for statistical purposes,
the tracing of protocol violations, and automated recognition of user
agents for the sake of tailoring responses to avoid particular user
agent limitations.