I don't think Haener's suspension explains much with Taysom's designation, I don't think they are totally related. Whether Haener is on the roster or not, you gain an extra active slot by designating Hill a QB and putting him in as the #2 QB during the game and designating Winston the emergency QB who doesnt take a roster spot. Haener being suspended just means that for the first 6 games you would not have had the option to argue Hill was a TE, keep Carr, Winston, and Hill active, and argue to designate Haener the emergency QB on the basis that Hill is not a QB which the NFL could argue as long as Hill takes QB snaps. But if you really wanted to play that card, you could still have played it the other 11 games much easier if you didnt actively designate Hill a QB now.

I think its possible the emergency QB rule was written with a 'screw the Saints' aspect. Its possible the league would have considered Hill a bona fide QB no matter what we did, because he played QB in college and had more QB snaps and starts than any other converted QB in the NFL, so the league could take that advantage and turn it in to a disadvantage where every other team gets an emergency QB but we can't advantage because our TE took too many wildcat snaps before the rule existed so he disqualifies us from having an emergency QB unless we make him our #2 QB. The Saints might have been expecting to be able to have Carr and Winston active, Hill active as a jack of all trades, and Haener as the emergency QB until they got the fine print of the rule, then realized the fine print prevented that, then decided making Hill the #2 QB for in game replacement purposes was their best option. Arguably the Saints were actually better off before the rule existed. Before the rule, no team got an emergency QB, and the Saints were free to use Hill however they wanted without disqualifying themselves from a benefit available to all other teams.