True especially if onboard subs have plate amps which use your main amplifier via high level as their input stage. They will take on the characteristics to a great degree of the main amps. That said there are fast and extended tube amps down below. More circuit dependent than on tube type IME, given an appropriate loudspeaker or succeeding stage to drive of course.
Jack-You hit the nail on the head. My speakers are exactly as you described and you hear the difference in the bass with every amp you hook up to the system. After hearing nothing but tube amps driving my speakers for years, hearing the first SS amp was an ‘ah-ha’ moment. That is when I learned my speakers love power and that there is another world of bass that exists outside of tube amp bass.