Unless you are sending full size lossless image formats for people to look at then while that’s an extreme way of putting it, yes. JPEG exports and scaling for displaying on websites etc will likely remove the subtleties of your image.
When you produce your image you reduce it to a stream of bits that are then interpreted at the other end for display. The only place you can guarantee it will be interpreted and thus displayed exactly the same is if you display it on the monitor it was created on.
So while I think they may be mildly interested, I think in a blind taste test, they probably wont notice the difference on the their monitors in the same way that when looking at an image they cannot tell which camera you used.
For the “photo industry” yes they care mainly as they are printing for an expected output media - for billboards, magazines, fine art for galleries etc. In which case getting as close a rendition to how it will look on their target output media is a valuable exercise. Having said that, when preparing for printing on matte paper, typically you turn the brightness down rather than up. Brightness and saturated colours are more like the output for glossy magazines.
I think in short, people care, it just isn’t a game changer - yet.
@r.harris1 puts it more eloquently than I am doing sorry.