Moreover I've found that a perception of mushy bass seem to inevitably obscure details in the highs to me, so I tend to think these two go hand in hand.
This has not been my experience.
A clean non-boomy bass and accurate instrumental timbre are the 2 key things I look for in a speaker.
Back when i was last looking for a new speaker, in the mid-1990s, room compensation software was little used, maybe unavailable, but the bass quality of the speakers I auditioned - all full range, that was a requirement - varied markedly.
The ones I chose had very clean bass (and still have).
The one that disappointed me most, as in it was enjoyable in other ways, had intolerable, to me, bass but lots of people love it.
One thing I noticed when Devialet started publishing the natural and SAM corrected bass response of the speakers they had measured this particular speaker had very overblown bass and the SAM correction reduced it whereas on most speakers it needed to increase the bass to correct it, and on some hardly any correction to the bass was required at all.
Whilst the room and particularly the position of the speaker in it does have a profound effect on the bass response it is not, by any means, the only one in my 50+ year experience.
Getting it fairly OK is easer nowadays but I am firmly of the opinion that an accurate speaker positioned to minimise the worst room excitation will still sound best when compensated, if only because the compensation won't need to be huge.