Do the big guys (Google, Microsoft, etc...) remember all HTTP clients and more importantly, the User-Agents that connected to them?
If so, should you implement this as a startup? (make your server remember the clients)
I'm not asking for advice, only for practicality or if there's some protocol somewhere that requires it. Like what's the standard, not your opinion.
The standard is: if there is data you need then you collect and store it. If you don't need the data then don't bother.
That information is in the request header sent by the browser. Anything the browser sends to the server can be collected, processed, stored, etc...
There is no protocol that requires it and you do not have to store this information.