Bad side effects caused by participating in other trials would happen with equal frequencies in the control group.

You just end up with a matrix of treatments. Whatever results you observe from someone undergoing treatments X & Y goes in the "X&Y" box, not the X box and the Y box.

But you would need much more participants in all trials, to make up for all those new combos that you now have to consider.

Also: I can imagine that most of the patients would be eager to engage in all possible treatments. You might not even have a control group that did not participate in the study of the faulty drug X

Then all you get is data about the effectiveness of XY. Would it be any better if only X was tested, but it turned out that that one drug 'X' contained two separate active ingredients, each of which the pharmaceutical company thought would probably be an effective treatment?