To be fair, it's better with a new deck. Tamariz's book provides a method for shuffling with faros and overhand shuffles from new deck order to mnemonica, and it lets you show they were in new deck order first and ended with an entirely shuffled deck.
I know. It`s one of my favorite books. But to be honest, you can`t get that easily into Mnemonica stack without some rearranging from a standard american(bicycle) deck order, but it`s possible right out of the box with decks which come in Fournier/European deck order (such as the Phoenix deck). Nevertheless, I think the strongest thing is not to go from NDO to Mnemonica stack, but to show in the end, after working with the stack for a while, that the cards are in NDO. The preshuffled cards eliminate the need of the faro (or antifaro) and rearranging methods to go right into the stack. I don´t do such long routines as Juan does, and he often goes into Mnemonica stack stepwise, while doing some other performances. I prefer a more direct way.
That`s why I think it`s sometimes nicer to have them already preshuffled in Tamariz stack order. You open the deck, do some 'honest' false shuffles without the need of any faros or Anti4-Faros, do your stack magic and in the end, all the cards are in NDO if you like.
In the end, 'better' is relative and I´m sure David Blaine hasn`t a table ready when working on the streets and he don`t have the time to bore his audience with some faro and rearranging sequences just to go into Mnemonica stack from NDO, so it`s logical he prefers the deck already preshuffled, no ?