I do some television production work out of the area, so this topic piqued my interest. Each time I come back to town - this is something I do happen to catch when I see what changes have occurred on local tv.
To your point- this generally has been the case over the past number of decades, since the backdrops were actually physical - something on a curtain that could be changed out for day/night shots or shifted on a duratrans background based on what the situation called for. Over the past decade, and especially the past five years, this has changed a fair amount with more sets in the round - ones that are more friendly to HDTV cameras and televisions, and ones that have large wall-sized screens serving as a backdrop.
From what I recall, most of KPRC's shots of the skyline are actually from the northeast (with Catalyst and I think Aris among others, frozen under construction circa 2016 or so).
I think KHOU has used more of the views from the southeast, as if you launched a drone from around Discovery Green or the Toyota Center for most of their background shots in the evening, but more of the traditional views earlier in the day - though 609 Main is visible if you know where to look. It may have been mixed up since they've moved into their new digs, but that's just what I recall.
KTRK is the only only one that I recall that actually tries to use a live camera on occasion - an aerial view from Memorial Parkway at Waugh, I think atop Memorial by Windsor. They tend to get some good sunrise & sunset views from that vantage and it looks well when they don't use the static views for the different dayparts.
KRIV has static shots of the skyline from the traditional view for all timeslots, but they are up to date with 609 visible as well as the most recent lighting changes to 1600 Smith.
Again I don't live in the area at the moment, and I don't watch streams unless there's a big event happening - so that's just generally what I recall as of a couple of months ago.
Of course as you said old photos not being updated aren't a new phenomena. Even when technology was used way back, there were a few faux pas moments that could be seen - if the viewer paid attention. KTRK is a good example of this with Heritage Plaza prominently displayed, prior to topping out from 1986 or so all the way up to 1992.