My experience doing that is that this is not common practice - talking about following up on a reference to find it actually refutes a claim, or more commonly that a citation has little to do with what it is being cited for (more extrapolation than a completely inappropriate use).
I agree with your should, but I do not think it is a realistic expectation right now.
As I see it, even if the only positive impact the ChatGPT ends up having on the world is in forcing researchers to double-check citations, then "mission fucking accomplished".
There are so many garbage papers in various venues that maybe it's a good idea. It forces readers to check them too, this puts them all on the lookout.
But in practice people are more likely to read you if you cite them. Furthermore reviewers are more likely to accept your paper if you cite the papers that they think are important. So the INCENTIVE is cite as liberally as you can.