I wouldn't mind it. Put it in May and maybe you could stop the campaign season from starting so early. It's really the only way to give everyone an equal say. I'd try it with an instant-runoff ballot so nobody wins without a majority vote, this would shelve the role of the delegates in picking the nominee. Or you could award delegates proportionality and then let them battle it out at the convention, fun.
People can give you good reasons why it's a bad idea though.
If all of the primaries were on the same day, I hope that we wouldn’t have an instant runoff. Several candidates would win primaries, and no one would win a majority of the delegates. The convention would be more suspenseful and exciting, causing more people to watch and hear the great republican ideas. When the 1980 Republican National Convention started, four candidates had delegates, and no one had a majority of the delegates. In Nov., Reagan won about 40 states.
The biggest problem with a national primary day is tha tthe candidate with the most money would almost certainly win. It would be almost impossible for a candidate to have grass-roots efforts in all 50 states, and an insurgent wouldn’t be able to, for example, win in Iowa or New Hampshire or South Carolina and then have enough time to raise funds and compete in other states. While it doesn’t seem fair that IA and NH always go first, it would be far worse if all 50 states voted on the same day.
“It’s really the only way to give everyone an equal say.”
Yes, I agree. There’s really no reason IA and NH should hold so much “sway” over the rest of the nation.