The tone vs no tone debate is an old one. When jazz was first recorded the bass drums were taken away since they’d make the needle jump on the recorder. Sort of like dancing in your living room to vinyl and the needle skips from the vibrations. Same thing, except for all time, so bass drums bye bye. Music? Oh yes, the music still got across just fine and was as popular as all get out and led/leads to the popularity of all music US derived to this day. i.e. your “tonality” is of no importance. You can say “it’s more natural/better/the drum’s intention” all you want but music will trump you every time. What serves the music? Tone? great. No tone? also great.
To answer the op’s question though is to fall into the same trap – separating music from how it was made. If music is made with either a live or dead drum sound is of no concern to me, at least now. When I was younger it was more of a concern, and the best example is the Miles Davis europe recordings from ’67. This was not on Tony’s famous K and 18 Gretsch. He dealt with backline and had A’s and other kits that were deader and not “that sound” that everyone loves. I hated it! Yet. The music was off the chart. It was (for me) the best music that band made, and it makes sense given the timing. They were at the end of what they could do. Tony was about to quit and do the rest of his life. Miles, same. It was the apex, or maybe the “I don’t give a f about anything” fall off from the apex. One of them called it anti music, but I think only because it ignored the rules of catchy melody harmony rhythm. Funny though that “tone” was not in the equation. Music was, and is, everything.
Another great example I came across recently: Hideo Shiraki's album Sakura Sakura. Really nice tonal sound, you can hear so many fine details, feels like you're right by the kit. Plus, it's jazz featuring koto!