So basically you have the right scared of former presidents being unjustly targeted in a way that threatens the democratic process, and then you have the left scared that the immunity will itself threaten the democratic process/enable dictators and corruption. Unjust use of prosecution as a political weapon vs just plain corruption being shielded.
It sure seems to me like it would be better if these matters could be handled on a case by case basis rather than in some black and white "former presidents can" vs "former presidents can't" be prosecuted way, but perhaps that is what will end up happening, not a legal expert.