Actually, yeah, it is frustrating... Many power settings are to a temp, and that means either accepting a difference or not. These two engines have common history, the other plane with common history matches remarkably, as in pretty much exactly.
In the end we respect the ITT limits but set equal N1s with one engine as a master, this clunker having no sync for the reasons you note, but look for reasons that the display is as it is.
I used to fly the Lear 45 with TFE-731s, it was long enough ago I don't recall many of the finer details. We did have engine sync, could couple to either N1 or N2. I don't recall ever being temp limited in that one engine was operating hotter enough than the other to the point it would affect operation. Same in the 737, the EEC does all the work determining thrust setting based on ambient conditions. The only time I've ever been limited by ITT was flying turboprops, we would set power by torque unless we hit maximum ITT then that would be max power for that current condition. If the engine "temped out" before reaching a minimum torque value there was something wrong and maintenance would have to look into it.