The Marianas Trench is the deepest part of the world's oceans, a pressure of 1,086 bars (15,750 psi). Yes, I agree there is possible life at crazy pressures in liquid water. Atmosphere of Venus (92 bar), so on earth we have life already documented at near 10x the pressure of venus.
This is consistent with what I was trying to say, may not have been so clear. But on a scale of -200c to +2000c being in a narrowband is water, correcting for temprature/pressure and state condsideration.
That being said, life detections in mariana trench are quite recent. Not likely to be detected by a simple probe of the type sent to mars, etc.[1] Highly specialized equipments. If I was looking for a needle in a haystack, it seems to make sense to find some haystacks first. And then rank-order the haystacks. Having a wider temp band means more haystacks, not neccessarily nore needles. Or easier to find the needles. If I had enough "protein" hospitable haystacks, I might look there first.
[1] The weight of a 1000 bar crush-proof engineering structure, and sophistication of communications and energy systems would be well beyond that curiosity, etc. Curiosity is of course not "simple" in its functionality, for what it does. But it's designed to spec for a unique mission.