I think the danger is that HFT will make HF bands valuable and there will be push to acquire the amateur bands.
Let me be a little bit pedantic here. High power itself does not cause interference, assuming that the unwanted sidebands are sufficiently suppressed. That is an engineering challenge, because modulation of any sort creates sidebands that put power on either side of the carrier. Higher modulation rates lead to more power in the sidebands. Secondly, any non-linearities in the power amplifier chain will also cause unwanted sideband emissions. That said, keeping your unwanted emissions outside of your allocated spectrum down to legal levels is "only" an engineering challenge. So the question to ask here is at the power levels they are asking for, is it practical to construct a transmitter that will keep unwanted sideband power down to acceptable levels?
A second issue is on the receiving side. And this gets challenging to explain easily -- but there is a concept in receiver design called "dynamic range", which is the difference in received signal strength between "minimum detectable signal" and the point where a strong signal causes 3dB of gain compression to set in at the first receive amplifier. A second concept is reciprocal mixing and 3rd-order-intercept, but I won't try to explain -- the bottom line is all receivers have a limit to how much undesired signal they can reject before the receiver front-end becomes non-linear and starts creating undesired mixing products. The undesired signal transmitter may be perfectly clean and legal, but the receiver on the other end just collapses like a gym bro that tried to bench too much. Part of the FCC's mandate is to make sure that users of other spectrum, using reasonably-well engineered receivers, can survive in the RF environment created by transmitters in unrelated spectrum. To put into other words, transmitting a perfectly clean signal that is so strong that it is impractical that, say, a consumer-price-point broadcast radio receiver has no chance of surviving should not be allowed, and certainly the commercial broadcasters are going to object.
However a sharp notch is a real pain to make in analogue domain. Lots of stages, temperature changes the component values, and things get bulky.
As a practical matter, interference complaints from hams are not easily or quickly resolved. Interference from power companies is difficult enough, and they want to know when their equipment is throwing sparks!