As far as I can tell, this is completely qualitative.
Clutches (including lock-up clutches inside torque converters) contain vibration dampers that are only capable of absorbing so much crank-speed irregularity. If the revs are low enough and the torque request is high enough to overwhelm those, you're going to feel it. One of the things done inside modern automatic transmissions to boost their efficiency has been to install serious vibration dampers so as to allow the revs to be brought further down at full torque with the converter locked before those vibrations start to be felt. (old skool lock-up clutches weren't even strong enough to hold full engine torque at any revs)
Same goes for the engine mounts.
I'm sure the calibration folks will discuss knock thresholds and mitigation - the need to delay ignition timing at low revs and/or run rich near full load to forestall knock, even though it also cuts torque output.
My motorcycle engines are unhappy below 4000 rpm if you ask too much of them, and they'd rather see 5000 plus, and for that matter, they'd rather see 7000 plus. They don't really get on the cam / on the pipe (exhaust) until they're spinning fast.
If you're clever with the accelerator pedal while climbing a hill, the Pentastar 3.6 V6 in my van can be dragged down to 1100-ish rpm in 6th gear at (near as I can tell) full torque with the torque converter locked. Obviously if you ask any more of it whatsoever, it does a downshift. That isn't in a favourable part of its torque curve, but in the interest of fuel consumption, it tries to stay in higher gears and lock the torque converter as much as it can.