It's a bit of a can of worms (but you're right, I should have said "deck/discard pile manipulation").

Shortcuts are supposed to be used to speed up and smooth play, there should be no information exchange, and so as another person pointed out this is about being able to describe all intermediate game states. If shuffling means you will reveal (seemingly) irrelevant but arbitrary information about your deck (e.g. cards that are no longer in it because they were discarded), you can't describe the intermediate game state beforehand (it is random) and the other player can't make an informed decision about whether or not they'd interrupt. And if you could infer from their refusal that there is a situation they might interrupt, you'd have extracted information you shouldn't have had access to. Hence in tournaments it is not allowed.

The deck shuffling is relevant due to other factors. There is a card in the combo deck that reshuffles the discard pile into the deck when it's put to discard, and the deck revolves around (as a shortcutted, freely undertaken combo) dealing one damage every time a certain creature goes to the discard pile. As you re-shuffle every time the 'engine' piece is hit, you can't predict how many times you need to activate the discard combo, so it cannot be shortcutted. Shortcutting in magic requires stating exactly as many iterations as will occur and the clear end state.

Slow play is the phrase explaining why indeterminate combos don't get shortcutted. "An indeterminate-loop combo may take anywhere from fifteen minutes to fifteen hundred years to actually succeed, and we really do not need to be waiting around to see which it's going to be."