Not at all true.
2000 watts to the MT is too much imo based off the voice coil, 2000 watts to the Ti is about right for daily driving. You'll break your MT with 2000 watts RMS, in fact, you'll even break the Ti with a 2000 watt sinwave a few a few minutes. Subwoofers really don't handel the power people think they do. Its hard to tell because music has so many breaks and pauses in it to allow the glues and metal to cool back down, but a continuous 2000 watts sinwave is pretty much death for any driver in the world. Burping and SPL competition is another story.
Not having power to drive a speaker has much more to do with the sensitivity of the driver rather than the size of the coil/motor. The Ti pro is 91.8dB with 1 watt at 1 meter in IB, and that is pretty darn sensitive for a 15” SPL subwoofer.
I don't have a working MT to give you a comparable number, but it should be very close from what I have measured with a working 18”.