I'm not suggesting you use it but (as for how it works in general) look into how Microsoft's Active Directory works. They've had the "service discovery" problem figured out for going on two decades, including preferences for "closer" servers, weighting, and so on.
I'm no MS fan by any means but AD is one MS product that really is awesome.
I didn't mean to suggest that they had some revolutionary new unique way of handling service discovery or even that they were the first. I think maybe you misinterpreted or misunderstood my intentions.
LDAP and Kerberos of all implementation are probably the most common use case for SRV records, most people probably don’t even know it. Real shame, in many ways I wish A/AAAA records weren’t even a thing for the vast majority of services (HTTP, I’m looking at you!)
Browsers do not own the A record and should never have been using it in the first place, so to continue squatting them and invent specious reasons for doing so is simple arrogance and assertion of unwarranted privilege.
Instead we have the multiple warts and misbehaviours of misusing the DNS for URL endpoint resolution.