I'd much rather that they become an informal "think tank" which can advise the current President.

Would that include Dubya?   I'm reminded of "Oh Brother Where Art Thou" where the Soggy Mountain Boys are appointed as the Governor's Brains Trust. Except that Dubya wouldn't come off well in that comparison.

What's so special about Presidents that makes them particularly unfit or for that matter particularly fit, to be a Senator? They're both just jobs in the service of the sovereign people.