Having been an "investigator" in a few phase 3 and 4 trials, it is true that all actions involving subjects must strictly follow protocols governing conduct of the trial. It is extremely intricate and labor intensive work. But the smallest violations of the rules can invalidate part of or even the entire trial.

Most trials have long lists of excluded conditions. As you say, one reason is reducing variability among subjects so effects of the treatment can be determined.

This is especially true when effects of a new treatment are subtle, but still quite important. If subjects with serious comorbidities are included, treatment effects can be obscured by these conditions. For example, if a subject is hospitalized was that because of the treatment or another condition or some interaction of the condition and treatment?

Initial phase 3 studies necessarily have to strive for as "pure" a study population as possible. Later phase 3/4 studies could in principle cautiously add more severe cases and those with specific comorbidities. However there's a sharp limit to how many variations can be systematically studied due to intrinsic cost and complexity.

The reality is that the burden of sorting out use of treatments in real-world patients falls to clinicians. It's worth noting level of support for clinicians reporting their observations has if anything declined over decades. IOW valuable information is lost in the increasingly bureaucratic and compartmentalized healthcare systems that now dominate delivery of services.

This could at least be done after release, but I don’t think any incentives are there, while collecting the data is incredibly difficult