I get that you like New Day, I'm a fan of them myself, but, c'mon, you only want to see this happen because you think it'd be cool rather than because it makes any real sense. If you'd be willing to take it this far, then you might as well come up with something for New Day to have the US and Divas Championships as well so they'd have all the gold.
The only scenario that might POSSIBLY, and I do mean POSSIBLY, have any potential merit would be for a member of New Day to win the WWE WHC MITB briefcase, cash in, win the title and for New Day to invoke the Freebird Rules bit with the WWE Championship. It'd certainly be a novelty as nobody has ever done that with a main event championship, at least not that I'm aware of, but just because it'd be a novelty doesn't mean it'd be a good idea. It's something that could work out and it's something that could be flat out lousy, it's hard to say. New Day is over, there's no debating that, and they might have the goods to pull this off successfully. At the same time, however, fans can be fickle and while they might have no problem with factions doing Freebird Rules with the tag titles, fans do hold the main event to something of a higher standard, and rightfully so; it was a novelty for Santino Marella to be US champ for 5.5 months back in 2012, but it wasn't a particularly good idea nor would it be for him to have won the WWE Championship.
As I said, this is something that New Day might be able to do well, but the odds are pretty long and even longer that it'd even happen in the first place.