You have helped identify WHY what you think is correct... when you normalize a signal close to clipping in the digital domain and then perform mathematical computations on the digital representation of that signal, the resultant value will grow as a result of the computations resulting in an overflow or saturation condition. This is why, in many applications such as digital mixing consoles, pre-conditioning may be part of the computation to prevent word overflow.
This is not the same thing as clipping of an analog signal that is being processed in the analog domain, though this TYPE of phenomenon occurs IF the gain-bandwidth product is not high enough to perform the differentiation because of the high amounts of global feedback necessary with most filters.
Fine, don't normalise. Just compare peak levels before and after. No, it's not because of loss of precision. Any competent DAW these days runs a 64-bit bus internally (or at least a floating point 32-bit). If it were such a thing, there would be a difference in the least significant bit (or close to it) between before and after filtering, which will never account for the usually 1-2dB difference between the two. This is a consequence of all minimum phase filtering, as opposed to linear phase filtering which is notable for preserving the waveshape (which is why linear phase filtering is preferable, for instance, in certain medical applications, eh. EKGs), unlike the former.
I stand by my experience that we are pathetically insensitive to absolute phase, the many lab tests that I have performed where the signal generation can in fact shift the phase relative to points in time, the difference is not even slightly audible. IMO, what you are hearing is due to something different, perhaps intentionally or unintentionally part of the hardware/software you are using.
Again, in the bass frequencies I think you are mistaken. I can't provide sources right now because I'm on my phone, but I will do my best to come up with one.
HPF's are very commonly (as in I don't know of any powered subs or processing algorithms that don't) used on pro subs to protect them from abuse and to improve the in-band performance, are you suggesting that this is wrong too? Many bass amps do use HPF's because the industry discovered that they demonstratively improve the performance to players. I started incorporating them in the mid 1990's, but used them in pro audio products I designed earlier than that.
Did I ever say that HPF can't be beneficial? Of course it is, it always is, mechanically. At least when critically damped and lower Qs. Also, filtering and/or other processing (multiband compression/limiting, for instance, or even multiband soft or outright hard clipping) does allow you to optimise a design (take IK Multimedia's tiny monitor speakers; while they can't really compare to a full fledged speaker, they are astonishing on relation to their footprint. Also, essentially all Bluetooth speakers on the market). What I question is the need to actually *add* an HPF (eg. in the form of a pedal or something to go in the FX loop) to what is supposed to be a properly designed bass amplifier. As you said, manufacturers know what their products can or can't do (or at least they should). Also, how is the user supposed to tune it? Just set it to their own liking? That's potentially a quick way to provide false security.
Let's take it up a notch: what's the point of separate heads and cabinets? Really, ideal amps should come as a pair. Or at least, with the power amp (and preprocessing) inside the cabinet like the old Acoustic cabs. Only that way can you properly design and optimise a cabinet, since you can process the signal to be amplified based on the characteristics of the cabinet itself. Still, essentially *all* combos, except possibly for some modeling amps, are essentially just a regular head bolted into their cabinets. Why, I say? Because, as I said,
you can get away with not doing so (and it works well enough). Usually, what suffices is the head's "subsonic filter" (which is essentially a HPF tuned around 30Hz or so). An HPF is not going to protect the user from themselves. If the user *wants* extremely loud deep bass, they are going to set the HPF low enough not to make any real difference. So, all that is left is just either creative purposes ("I want a leaner bass, but the bass control on the amp takes away too much", and it's a perfectly valid reason!), room EQ purposes (as imperfect a solution it may be) or an actual knowledgeable tech working for their client.
HPF's on bass goes back over 25 years, when designers discovered that their speakers (that were much more limited at the time) sounded better and lasted longer.
HPFs have always been a part of amplifiers and you know it. AC coupling is done essentially with high pass filtering. And if you can avoid using electrolytic capacitors and high resistances, you generally do (makes for better reliability, usually, and lower noise respectively). This means that most of the time there will always be some part of the amplifier cutting somewhere, and that's repeated for how many stages you have in an amp (unless they are totally DC coupled, but it's rare).
Since this is a bass guitar forum, equating mastering techniques doesn't really apply. For mixing consoles, most that I have measured are pretty close to critically damped with peaking under a dB.
Mastering is not too dissimilar from mixing, in a sense, and what I said applies to mixing too. Having a peaky HPF is done purely for creative reasons, "because it feels fat". A plugin I use, TDR Slick EQ GE (billed as a track or bus EQ), provides two choices of HPF, one critically damped, the other underdamped (you can't even choose the Q - it's meant to be some sort of "analog emulation software"), because a common trick is to high-pass kick drums with a peaky HPF somewhere around 50-70Hz, and maybe saturate the result a bit.
A properly designed ported cabinet accounts for the unloading, but this occurs below the tuning frequency not at the tuning frequency. Bass most certainly can have significant energy below 60Hz, perhaps you are mixing your instruments up. A sealed cabinet reduces LF excursion but at a cost of reduced LF energy which resuolts in the need to turn the amp up which negates much of the benefit. Biamping wasn't successful because once LF drivers and cabinet design improved, it was more trouble than it was worth.
Did I say "at the tuning frequency"? If I did, I obviously meant below (and it really is immediately below, even just 4-5Hz away means exceeding Xmax abruptly). Anyway, guitar instruments are strongest in their second harmonic, which is proved by the fact that you can filter away the fundamental and it still sounds fine (which means that the fundamental isn't generally that strong to begin with). If it weren't so, the very idea of a HPF on bass set higher than 41Hz would be absurd except for some "old radio" kind of effect.
And finally, why would bi-amping be more trouble? Any PA system is at least tri-amped (subs, midbass, tweeters). The cheapest two-way speaker used at karaoke bars is bi-amped. Even with a separate head and cabinet, it would only mean having two cables instead of one (and it's not even necessarily so). It's not about trouble, it's about having the coloured response of an outdated technology such as that of a bass cabinet (or a guitar cabinet for that matter). What is done in MI amplification exists essentially nowhere else. Even just the 4x10" or 4x12" layout makes little sense, stack the 4 speakers vertically in two cabinets and you have much better dispersion (at least below 3kHz or so, without having midrange drivers) as well as having speakers at ear level or closer to this, being better able to judge your tone. On the other hand, many people actually like the fact that they're hearing a lowpassed version of their amplified sound by standing over their amp, or they like the fact that you can move one step sideways and bass/guitar disappears (so they have control on their own volume, which they can keep at ridiculous levels without causing too much inconvenience on the others).