I also listen to the hammer strike, the initial overtones, and their decay. Instructive in terms of how the system handles the whole sonic envelope, not just wide frequency range. I’ve had a couple very good pianos, including a vintage Bosendorfer. You can make easy comparisons by ear with the live instrument and a recording. (Every piano, even the same brand/model, tends to sound different. Someone who restores these instruments knows how to voice them to achieve different tone and attack).
The trick is finding good recordings. Either the piano is too closely mic’d or is presented in miniature compared to a full sized grand.