There are lots of problems with the US Primary system. But one of the advantages of the system as stands is that a relative unknown can make a big splash in the early ones, building momentum as the season progresses. Of course, this hands very significant advantages to Iowa and and New Hampshire. But having all the primaries on a single day would mean than only people with LOTS of money and support stand a chance. This guarantees your selection is limited to 1) party favourites, 2) billionaires, or at least multi-millionaires, or 3) people specifically in the pocket of powerful interest groups.
This would be far worse than the current system, as bad as that may be.