I have worked on about 30 Surfaces for this issue and I can tell you this:
All Surfaces were able to be fixed with the correct updates and calibration technique (except two that died whenever power was disconnected).
Some just needed the correct update/calibration procedure.
Some had to be reset in order to remove any system firmware updates installed before the November 2016 firmware update, but worked fine after all correct updates were applied and the device was calibrated.
(firmware updates can't be uninstalled, but the November 2016 firmware update overwrites the previous firmware updates that REALLY MESSED stuff up, and the overwritten updates/files have to be removed, but can't be uninstalled, so you have to reset)
As for the two that I couldn't fix:
Both devices would shut off when unplugged. No matter what the charge said, or which update I applied. A reset wouldn't even fix it. They still died when unplugged.
Microsoft charged one client $450 to replace it (old and out of warranty and before it started happening to EVERYONE, so Microsoft was still able to play it off like it was just old. I argued and argued with them (because I knew the symptoms of the updates and how they behaved) until they agreed to replace it for the cost of it being under warranty.
The second client got his Surface replaced for free. His was still under warranty though and it was some time after the issue was finally recognized by Microsoft.
It was so frustrating when this started happening, because Microsoft wouldn't even admit there was a problem, but after a LOT of research and trial and error, I figured it out.
Microsoft finally got the update right, but won't bother telling you the correct procedure on how to apply the update.
So, have hope!
Side note about replacement Surfaces: These are sent out with the battery/overheating issue. So don't think a replacement is gonna be ready to go when you get it :)