Depends on what the study is trying to prove. You seem to be angling for some sense of "fairness", as if this is a game where EV / ICE "compete" and we want the rules to give each side equal chance or something like that. This isn't sport; if you're doing a scientific study you only care about getting the correct answer to your question.

If your question is whether a second-hand BEV has higher / lower environmental cost, why would there be a problem doing such a study.

It's not a foregone conclusion either; e.g. (hypothetically) a lifecycle analysis could show an EV to be less optimised for long-term use (spare parts environmental cost, etc.), compared to a new ICE with a more sustainable long-term maintenance story. This might be unlikely but you can't find answers to these questions without such studies.

The original claim was "All EV's are worse for the environment than buying a used Petrol car". If your claim is that buying a used EV will be best of all then that seems reasonable.