And if Scotty invented transwarp beaming then why didn't Picard know about it?
Because Scotty only perfected his transwarp beaming formula years after "Relics"
Come to think of it why didn't PrimeSpock use transwarp to transport himself to Romulan space with the red matter to save Romulus? You bastard Prime Spock. No wonder Nero hates you :shakes walking stick in the air:
Because of the danger factor - first time they used it, Scotty almost died. He described transwarp beaming without a recieving pad as "trying to hit a bullet with a smaller bullet whilst wearing a blindfold, riding a horse."
OK maybe there's some limitation on it. Or maybe Scotty showed Spock the formula but didn't actually build the transporter. But if Khan did, then no doubt Spock could.
It's all software, like the modifications in TNG's "Birthright" or DS9's mirror universe episodes. Think back to all the crazy stuff transporters have done over the years without any changes to the default hardware...
-splitting Kirk into good and evil halves
-beaming into a parallel universe
-making a copy of Riker
-De-ageing Picard, Ro, Guinan and Keiko to children
-Making Hoshi into a ghost
-Merging Tuvok and Neelix into Tuvix
-Unmerging Tuvix... months later!
-Beaming across time in Deep Space Nine
-De-ageing Pulaski and curing her disease
-De-ageing Kirk and Spock in the cartoons
-Re-ageing the bridge crew after an alternate reality de-aged them in the cartoons.
-Beaming across space and time several times in TOS
-The Dominion had a transwarp beaming equivalent in DS9 and used it several times
-People getting lost in the beam, only to be seen by Barclay as floating monsters during teleport.
-Scotty spending 70 years dematerialized inside a transporter.
-The transporter inventor's son becoming a ghost that mutilated people when they touched him. He spent 18 years like this.
THEY are why transwarp beaming is no big deal whatsoever, and perfectly consistent with the Trek universe. I can only imagine the reaction if they dared resuse one of the other ideas above