Re. subtlety: The early days of TNG were particularly egregious, by having the Enterprise visit other planets and cultures who were not as "evolved" as 24th century humans. Picard or one of the crew would arrogantly sniff their smug disdain at the backward little aliens, point out their faults and condescendingly browbeat and lecture them on how to be better people like them. Hardly any attempts at subtlety whatsoever.
It is more subtle to critique humans of ‘now’ by having ‘aliens’ in the future be slightly exaggerated versions who are shown the error of their ways by the human characters the audience identifies with to some extent, than have the human characters of the future behave more like the humans of ‘now’. That people feel they cannot identify with the ‘perfect’ humans of the 24th Century, or even at least aspire to do so, says more about us now than anything else.
The same is true of DSC and the modern shows, (and as you say, Picards crew to some extent in TNG) where it does sometimes seem the right to be an arrogant sod is something humans don’t want to give up. And no Q to pick them up on this. (Q does to Picard what Picard does to the Eloi. It might almost be a point being made...)