Do big subwoofers sound bad in small rooms?

except that the weight of a passive radiator is much higher than that of the air column in a port

For a typical BR spec vent size, but IME (and IIRC also Tom Danley's) using a simple BR vent's air mass to find the weight of a PR is spot on when using the correct air mass density and of course when the vent area (Av) = the PR's effective piston area (Sd), which due to it needing an ideal ~> 2x driver effective piston area (Sd) dictates a ridiculously long vent (Lv) to reach down into the (sub) bass.
 
And that does not take into account the dramatic reduction in box vibrational load. The benefit of that is HUGE.
I will testify to that, from some fiddling with our SVS SB-2000 Pro. We like it very much, but wow it shakes at high SPL. I mean as a loudspeaker engineer I knew that theoretically, but seeing and feeling it was really a shock. I would really favor mechanically opposed designs in the future, though AFAIK there are not so many choices (??).
 
I read somewhere, don't remember where, that subs need to be bought according to room size
Subs? Or speakers? I read that myth often about speakers. Myth started by unfortunate coincidences. Yeah in small rooms modes start at higher frequencies so a less extended response from the satellite speakers could sound less bloated in some cases. For subs, if the crossover is well set, it shouldn't be an issue, unless the sub is tuned kinda bloated which surely some are. My preference for subs or satellites has long been "undertuned" designs, with a port tuned lower than "ideal" to maximize the -6/-10 dB points* and have a rolloff more like sealed.
*as I've posted elsewhere, the -3 dB point was just a mathematical convenience and convention from electric filter design that Dick Small used in his original thesis. In a conversation we had in Indiana when he was working at Harman, he agreed in rooms the -6 or -10 points probably mattered more due to room gain.
 
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An 8" driver flapping around close to Xmax is never going to sound as good as an 18" barely moving, plus a larger driver couples better with the acoustic impedance of the surrounding air.
The late great Dr. Richard Greiner would have agreed with you. He had IIRC 4x15" per side for woofers, driven by some thousands of watts. And barely moving. (=less modulation distortions).
 
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