I have put ~8,000 miles on my 2026 1300RT in the three months I've had it. About one quarter of those miles with the sport windshield, the rest with the touring windshield. Also, the last few thousand miles are with a Remus slip on. This is my 8th BMW since 1973 and 4th RT .
It is notable that you have two cylinders, 13.3 compression ratio,145hp, 8 valves, shift cam and superior wind protection. It may be impossible to compare the sounds of that to a 60hp airhead or six cylinder engines. Also, the 1300 idles near 2000RPM for a few seconds when cold. If you start it in your garage before you put on your helmet and ear protection you are treated to a Bavarian symphony! ...in my opinion ;-)
Did you take a test ride? Did you hear the sounds then? Did you ask the dealer if that was normal? Did the sounds bother you then? That is a lot of money for a bike that "sounds like it getting ready to grenade"
As far as "Of note is the fact that K16 riders that have switched to the R13 talk of the increased mechanical noise!" Carl Sagan (among others ) said that extraordinary claims require extraordinary evidence. Who and where are these K16 riders? How many are we talking about? How did they measure this increased noise? Have their experiences been observed by neutral parties and documented? Where is the documentation? Have they relayed their data to BMW Motorrad? Those are just some questions that need to be answered in order to have extraordinary evidence.
In 55 years of riding I have enjoyed listening to other riders' stories and opinions on forums, in the shops, restaurants and rest stops. However, we should be careful of what we call "fact".