Actually, ears are very insensitive to absolute phase at low frequencies. Peaks will not get higher with a HPF unless the Q is unreasonably high (approaching an oscillator), and will always improve the headroom. A HPF set to 20Hz with a critically damped Q will result in virtually no different in tone since it's at least 1 octave above the cutoff frequency of 99% of bass guitar cabinets. It may help a little but not much.
This is demonstrably untrue. Take any audio file, normalise it to near clipping, then apply a simple HPF at 20Hz, even critically damped. Unless there is significant energy at infrasonic frequencies and between 20 and 40Hz, the audio file will now clip. There is a reason why in mixing and mastering audio filtering tends to be done at the beginning of the chain, and anyway the last step is always the limiter. Also, we are insensitive to absolute phase everywhere *but* low frequencies (and we are never *very* sensitive anyway). AFAIK, people can pick a high passed bass (or kick drum) in a blind test quite reliably, even when it's far below the lowest frequency they generate.
This is not at all true. Take a speakers rated at 400 watts RMS mechanically and drive it with an amp rated at 400 watts or more RMS and the HPF will improve the speaker's mechanical power handling at the lower frequencies. It will also reduce the distortion that's generated by driving a speaker below it's -6dB rolloff point (where distortion increases exponentially as the frequency falls).
Of course, it can't hurt. I myself apply a HPF on all my wedge monitors or 2-way PA speakers, since they are not really expected to produce bass. Still, pro speakers (which bass guitar speakers essentially are) should be able to take some abuse though. And also, the truth is, most bass amplifiers already include some high-passing anyway. Not to talk about bass effects.
As the speaker reaches Xmax, the lifespan begins to fall as the suspension components are being driven beyond their linear limits. The farther beyond Xmax, the shorter the lifespan, this is not the kind of distortion most players prefer either. There is plenty of well known math behind the lifespan curves, that's what knowledgeable manufacturers base their ratings and warranty periods on.
I'm not talking about grossly exceeding Xmax, or even constantly pushing the speaker around Xmax. If it's just on transients though the speakers *should* handle it gracefully (proved by the fact that so many old cabs are still working fine; HPFs on bass is a relatively new trend), with some compression that many musicians actually find pleasing (otherwise, again, there wouldn't be such a thing as "that cab need to be pushed to sing"). Of course, if a cab is grossly underdimensioned, it sounds choked because it will be distorting lots all the time.
A high Q HPF is not typical because it introduces tonal changes that may not be desired. MOST of the (successful) commercially available HPF's are in fact pretty close to critically damped (Q of .7). there are exceptions where the filter is achieving two things simultaneously, but that's not what we are discussing.
I was never discussing high Q HPFs in general, that was just a side remark (although many HPFs used in mixing and mastering are relatively high Q, with maybe a 2-4dB peak around the cutoff frequency).