You seem to misunderstand. Let's talk about an 15 kW asynchronous machine with two poles hooked up to a VFD. At nominal voltage (say 400 V) and nominal frequency (say 50 Hz) it will produce approx 50 Nm of torque to reach its nominal power (n ~ 2900 min^-1). Input current will be somewhere around 30 A. Let's say we want it to run at approx 300 min^-1, thus frequency is reduced to ~5 Hz and voltage to ~40 V. Output torque will still reach approx 50 Nm at the same current as it did at 50 Hz. However, output power is now approximately 1.5 kW. You can boost low-end torque a little bit, but not by much (every VFD offers some parameters for this), because this requires increasing the current.
If we were to run this motor "constant power" at 300 min^-1 it would provide about 500 N*m of torque and run at a hypothetical current of 300 A -- it's quite clear that that isn't going to go well.
Sure, there are lots of ways you can make a motor that will mess that up. You can put in current-limiting fuses. Many motors cool themselves with fans, so they can dissipate lots of heat at speed and will just burn up if you try to add torque. You can make windings with insulation that breaks down at low voltage so the motor can't spin fast.
For big stationary motors that are wound for high voltage, the large number of turns means copper losses dominate and limit torque at all but the highest speeds. Nevertheless, those motors can be rewound for lower resistance, which will cause them to have more even tradeoffs at different voltages/currents. Rewinding a squirrel cage rotor is... a bit of a task, obviously, but the torque/voltage constants are always pretty interchangeable.
If we were to run this motor "constant power" at 300 min^-1 it would provide about 500 N*m of torque and run at a hypothetical current of 300 A -- it's quite clear that that isn't going to go well.