Keep in mind that the all the TORA is not going to be used/available for the aircraft roll .. despite what might be inferred from the AIM definition cited.
Depending on the rules in play the use of TORR is that either one third or one half of the airborne distance from liftoff to screen has to be over the TORR .. ie the calculated ground run (which is transparent to the pilot in the AFM) never uses that last bit of the TORR.
ASDR, on the other hand, is serious rubber on pavement stuff.
Can TORR be limiting ? .. depends on the aircraft, runway and ambients. Usually, TOR considerations are hidden in the AFM calculations and, so, tend to be a bit of a mystery for pilots. Some AFMs will provide explicit TOR data .. just depends on OEM practices.