There's plenty of historical examples of how bad of an idea prosecuting former leaders is. When a country's leaders fear prosecution if they lose power, they have every incentive to cling to power as long as possible by any means necessary. Certainly there's a middle-ground that needs to be struck between the President they are above the law entirely and the President fearing prosecution by the next party in power regardless of how lawful they behaved. I worry that, in the U.S.'s current political climate without immunity, Presidents would be prosecuted by the other party as a matter of course.