It's more important to convict the rank-and-file anyway, IMHO. As powerful as the President is, corruption at that level requires a horde of Yes-men or co-conspirators to pull off.
If THEY know they're going to jail even if what they did stays hidden until years later, they'll be less inclined to do the bidding of a corrupt Chief Executive who tradition demands not be prosecuted if he manages to keep scandal tamped down enough to get out of office ahead of it. I kinda am okay with the soft "diplomatic immunity" model where you don't prosecute ex-Presidents, and only have impeachment to deal with alleged crimes while in power. The President isn't above the law, but let's be real, the power vested in them means for the time they hold the office it's unreasonable and unrealistic to think their legal status should be the same as a common citizen. That period of their life should remain encapsulated as outside the bounds of typical prosecution. (Typical not meaning "any" but, like I said, if he's fucked up bad enough, impeach him, and if you can't, then too bad, you lose the chance. No President should have to live under the constant shadow of purely political post-office revenge prosecutions when they're just back to being a "regular" guy.
Look at what they did to Trump for no other reason than base political disagreements and tell me removing those unofficial protections would not cause Banana Republic-level chaos as every President would be permanently embattled while in office, making decisions based not on the needs of the Republic but on appeasing those who are already plotting to be waiting outside the White House on inauguration day to slap the cuffs on him for rinky-dink charges that exist only to make him miserable in perpetuity after his term(S) for keeping them out of power for the last 4/8 years....
Not prosecuting a departing President for things done IN said Presidency is a necessary evil to keep the system functional. Because surely you can imagine the wild abuse you invite otherwise.