For example, look at the original Star Trek. The effects were very unrealistic, everyone knew they filmed planet scenes in the desert (not on a different planet), etc. But nobody cared, it’s still a cult classic.
Star Trek TNG is pretty much the same. Despite more advanced effects, everyone knows Data is just a guy with makeup, but it was much harder to think the Enterprise was not a real ship.
At the end of the day, suspension of belief depends on delivery of lines, acting, etc, and much less on CGI or “classic” effects. CGI just makes (arguably) easier to achieve the effects.
I think that's overly restrictive. There's nothing inherently wrong with flashy CG environments, elaborate action sequences, etc. even if they're largely "for their own sake." When conceived and executed masterfully, I want to see the flashy stuff too! Of course, it's also true that sometimes very rudimentary effects can work great to advance themes or plots (like in the Star Trek series)!
What's worse, the abuse of retouching is making real things look fake. I remember watching the ending of Indiana Jones and the Crystal Skull at the cinema and thinking "why did they chose to make the top of the pyramid CGI? It's so cheap." Later I discovered it was a practical effect, color "corrected" to the point of removing any resemblance with reality.
"Spielberg and his effects teams succeeded in creating convincing visual effects because they didn't rely on CGI as their go-to tool. In fact, only four to five minutes of the 14-15 total minutes of dinosaur scenes were entirely computer generated. All the other visual effects were created using Stan Wintson's various physical dinosaur models. The legendary technician, responsible for creating practical models for Predator and Terminator, built everything from animatronic puppets, to to a full-size animatronic T-Rex, and even Velociraptor suits that could be worn by stuntmen. CGI was then used to build on top of what the production team had already created on-set. In other words, Jurassic Park's CGI still looks so good today because there isn't much of it in the film, which makes sense considering the limitations of the technology at the time.
...
But perhaps even more important than the breakthrough graphics was Spielberg's decision to still keep the CGI to a minimum. According to Dennis Murren, visual effects supervisor at ILM, once the director saw how convincing the digital dinosaurs looked, he actually rewrote the ending of the film to include the now-famous full-body shot of the T-Rex letting out a final roar in the Jurassic Park visitor center rotunda. But despite clearly being impressed by the capabilities of ILM, Spielberg still limited the CGI elements and retained the use of Stan Winston's puppets for much of the memorable dinosaur scenes viewers still love today. In fact, there's said to be a total of just 63 visual effects shots in the whole film, a tiny number compared to Jurassic World's more than 2,000 VFX shots."
https://screenrant.com/jurassic-park-cgi-still-good-how-expl...
I'm struggling to think of really recent examples but one I recall when CGI was starting to have this problem, that was pretty subtle (to the point that it's easy to watch it and not realise how many small CGI effects are used, along with some physical ones) is What Lies Beneath. It's mainly to cover up the impossible camera angles and you'd hardly know.