I would say it is not completely true. If you have a game that works at 59fps (such us Wii U’s Mario Kart 8) or is continously losing frames (such as Xbox 360’s Dead Rising), you will experience stutter in the former and tearing in the latter. Those problems could be solved if an adaptive sync technology were implemented.
In regards of old consoles and old arcade cabinets, this happen to be a problem too. Some shmups and fighting games have been reported as “not so satisfactory” when used on LCDs due to their condition of fixed refresh rate displays. That’s one of the reasons why people still use 240p CRTs for tournaments and showcases.
I don’t know if this is too difficult, but if it is just an fps counter and a little bit of DisplayPort/HDMI 2.1 logic, it would be a nice feature.