I don't think they are that stupid.
Because that could require them to litigate every single act a president took while in office. Every single one. We would have to set up a full time court just to have all the hearings.
No one wants to open up that can of worms.
But sure, let's drag Jimma Car-ter into court and have him charged with offenses against the security of the US by shutting down Verona. For starters.
I have a real long list.
It would only take a couple of rulings for them to say those were official acts to shut down much of anything else being raised that appeared to be an official act by a President. The other options are worse - to say there is full immunity for anything a President does while in office (0% chance of happening) or that there is no immunity at all (what you are talking about - a deluge of cases prosecuting Presidents - would happen then).