Many of you seem to be answering the wrong question. The question is not "Should you let the spectator shuffle?" The question is why
it is considered a bad idea to give the deck to a spectator for shuffling or replacement after they have selected a card which is known to you (through force, memdeck, etc.)
That is, why is it wrong, after a successful force, to just hand them the deck and let them replace it themselves?
And the answer is that leaves the true
explanation, that you already know the name of the card, as the only possible
explanation. Roberto Giobbi
says in Card College One that
"One tendency that is particularly widespread is to hand the deck to the spectator immediately after the force, saying in a triumphant tone. 'Fine. Now replace the card anywhere in the deck and shuffle it yourself. ' This would make even the dimmest spectator suspicious."
Giobbi suggests that if you take the card back, do a brief overhand shuffle yourself, and then hand them the deck to do a spectator shuffle, that takes the curse off it.