It's odd that the code descriptions for P2714 don't match what Toyota publishes in TIS.
What's your mileage?
The explanation feels like a worst case scenario for a mechanic who doesn't want to try to troubleshoot and fix the problem. The dealer knows if they replace the entire transmission your problem will go away. As an IT guy who fiddles with mechanical and electrical stuff, debugging problems takes some patience and an ability to walk through potential problem points methodically. I would say the vast majority of ASE-certified (and Toyota-certified) mechanics don't have that skill - they are trained in how to determine what system has the problem and then how to safely replace it.
Several years ago Acura told me I needed a new Nav unit. The unit would freeze up, or on start would post a failure message. $3500 estimate. I decided to run the self-diagnostics and it showed the DVD player for the maps was not working correctly. I removed the unit from under my seat, took it apart, and pulled out the DVD drive... matched the part # on the bottom and ordered a replacement for $65 off
Alibaba. 3 weeks later it was fixed.
I would find a competent transmission repair shop. If a solenoid has failed it's going to be a couple hundred bucks to replace it. That's a far cry from needing an entirely new transmission, and the difference between swapping out an oil pump or a bad knock sensor vs replacing your entire engine.
Now in fairness you don't know the vehicle history and it's certainly possible someone towed a 10k # trailer in 6th gear over mountain passes and overheated the transmission, then continued to drive it afterwards without swapping the fluid, or flooded the vehicle in a river and then water ingress into the transmission diluted the fluid and caused this failure, but I personally would not drop $5k on a transmission simply based on P codes without someone walking through the manufacturer's troubleshooting procedure. Replacing the transmission based on a P code is like going under open heart surgery because your left arm is going numb - the codes are an indication there is a problem, but they don't necessarily tell you what the problem actually is and it's entirely possible something else triggered it (like you fell asleep on your arm) or that the sensor itself that sent the code is bad (like if you lost your arm so of course it's numb).
In fact in your case if there was water infiltration (i.e. fog lights that won't go off) it's even possible there's a wet wiring harness connector shorting out and causing multiple codes to fire incorrectly, in which case a $5k transmission won't even solve the issue.
