I want a sub that won't have any high pass filter in place, indicating that anything in the recording won't be lopped off),
I understand and agree with your principle to have a sub that is not limited by electronics (and/or driver capabilities). In fact, I am sure this is the end game for everyone on AH, to have a system without any limitation, or the best while considering limitations like, budget, WAF, geographic location, etc.
In context of subs with intentionally limited lower extension due to High pass filter, I can site
content that has signal at 5Hz. To extend your thought process, it is reasonable to expect that a given sub must handle any signal down to 1Hz with playback at Reference Levels while keeping distortion below threshold of perception. Since cost and/or size are usually the first considerations, there will be a tradeoff between SPL and extension. (All subs have seemingly huge distortion, albeit, below threshold of perception, which is a well understood and accepted tradeoff.) (There are folks who purchase/DIY build a speaker/sub with no consideration for cost and/or size, while only considering prestine sound quality, I have yet to meet anyone in my circle with this level of means.) (I want a display with the Black Levels equivalent a Black Hole’s Event Horizon

.)
but if there's content below 20hz, your sub is removing it in order to protect itself.
Somewhat correct because the roll off is not a step function and there are room and placement gains to be optimized. Further, this is not correct in case of the SVS subs when tuned for extension rather than SPL. SVS's (including mine) have a port tuning option (plugging the ports) with an adjustable setting for the low end HP filter's frequency. Mine is set for 15Hz ("The -6 dB point goes as low as 12.5 Hz which easily transfers into 10 Hz extension in a typical room", tested and plotted
here). The SVS is designed to give the
user the some flexibility in the tradeoff between SPL and extension (and using good design the distortion is already limited to below threshold of human perception), all the while ensuring that the amp and driver continue to operate within their specified limits. This concept is no different to a bookshelf speaker manufacturer having low end HP filter at 80 or 100Hz. I concede that those bookshelf speakers require a sub. (But, you have introduced signal processing by way of a crossover and summation of the L+R signals to a sub. I address that later.)
It's still a lot of bass, but it's being compressed.
I understand what you mean here, but, audio signal compression is a form of data processing designed to reduce the transmission bandwidth requirement of digital audio streams and the storage size of audio files. Information is intentionally removed (tradeoff between required transmission bandwidth/storage size and signal integrity aka quality). “Compressed” may not be the most appropriate term, rather, ‘processed’ which could mean, signal level is reduced. And that is exactly what is happening with a HP filter. The signal below the pass frequency is processed by way of being attenuated, not compressed. There is still output below the HP setting, and its level depends on the slope of the HP filter, box tuning, driver and amp.
To me an ideal subwoofer system doesn't do anything to the signal that isn't already there.
But then, how do you feel about room effect correction via, Audessy or YPAO or parametric EQs using a DCX2496. They are changing the signal information from how it was before ‘processing’, the signal has been changed. A Low Pass filter on the sub will change the signal, do you run yours without a crossover? Anyone setting their speakers to "small" has introcuded processing too. I suppose not all processing is bad, as they say, "use with caution"

.
If you were to hook up the driver in your svs to a 1000w amp with no other circuitry, would the results be identical?
Since the driver is designed to work with 500W max, I am sure a full power signal from a 1000W amp will fry the voice coil or rip the surround by pushing it beyond x-max. But, irrespective of the amp, controlled measurements on the driver will yield identical results assuming it is operating inside the manufacturer specified limits. Further, if the SVS box and driver are fixed in this experiment and tested under controlled conditions, the combination will yield fairly consistent reproducable results with different amps (assuming the amps are themselves not introducing variables).
More importantly, because you only have one sub, I strongly doubt you have the best SQ you could get, even with the heavy EQ alluded to earlier. With one sub i've measured a ton of different placement locations and never found anything close to +/- 3db frequency response tolerance.
And this is also true, my sub is equalized for the primacy listening position only (with my tradeoff being that I don’t care if others are not getting +/- 3dB down to 15Hz, because no one I know is as AH as me). I had used some room treatments and eq to control the peaks. And yes, my FR plots still leave a lot to be desired because my room is far from perfect.
The $2500 sub would still have had the ragged frequency response caused by the ROOM.... I absolutely disagree with this approach.
100% agree with you, but it still happens. Rather than get 2x$1000 subs, folks will get 1x$2000 sub for brand/bragging rights/perceived benefits. We are fortunate to have built up our knowledge and now understand the tradeoffs, most don’t. (I intended to have a 2nd Ultra within a year of the 1st, but priorities changed

.)