Yep.

And such studies already exist. One compared the myocarditis rarely associated with vaccination with non-vaccine myocarditis found "in nature."

They found that while regular viral myocarditis is typically a big deal, myocarditis following vaccination is usually very mild. This makes sense: heart inflammation is a response to viral infection, and vaccines are very weak viruses, so it's a much weaker response.

So when they did the comparison, they found that the problems resolved more quickly and more quickly. Viral myocarditis is unpredictable and can require a heart transplant, but the sample studied with vaccine-related myocarditis were able to get through it quickly with only painkillers.

https://jamanetwork.com/journals/jama/fullarticle/2788346

The problem isn't whether these correlations are being actively studied and established. It's whether or not people will trust that research enough to change their mind on taking a vaccine they're convinced will kill them.