Iowa and New Hampshire always going first is a problem. But a national primary is far from the solution. Indeed the larger concerns of all voters should be primary front-loading. A candidate who doesn't win one of the first four primaries that all occur in the first 4 weeks of the campaign will have absolutely no shot because a ridiculous percentage of delegates and big states all vote on February 5. This situation is made worse with a single primary voting day.
A national primary provides absolutely NO CHANCE for any candidate that hasn't raised $100 million and hasn't already been anointed by the media as a front runner. And putting the big states up front would create the same problem. Winning in a state with expensive media markets like California or New York would require raising similar high sums of money. The more money required to raise, the more difficult it becomes for $50 donations - average people - to have an impact.
Simply, it's good for the process to have a limited number of small to medium sized states vote first. But more states and big states need to weigh in early too. The solution is a longer primary process primarily from February-May.
Here's what a good calendar would look like:
EARLY PRIMARIES (Mid-January to February)
The first 5-6 weeks of the campaign primaries need to have 3 couplets of small/medium states (for six total states), spaced out on 3 dates in 3 different regions. For example, it makes sense for Connecticut and Rhode Island, or Oregon and Idaho to vote on the same day. It saves candidates money on ads since they would play in media markets that touch both states. It also saves money on travel costs and allows smaller campaigns have smaller staffs make a larger impact. For example, a Kansas City presidential office would have phone banks going into Missouri and Kansas. The point of this is to allow smaller, well-run campaigns that resonate with voters to actually compete - to make the nominee the best candidate instead of the best fundraiser.
January 15: Iowa & Nebraska
February 5: South Carolina & Georgia
February 19: Delaware & Maryland
SUPER TUESDAY (Mid March)
After the early primaries have 3 weeks of silence so candidates can campaign for the first Super Tuesday where 1 or 2 of the big states (California, New York, Florida, Ohio, Pennsylvania, Texas, Illinois) are mixed in with 4-5 other states. The silence gives candidates a chance to raise money, respond to media narratives, go to multiple debates, etc.
March 11: Ohio, Pennsylvania, Arkansas, New Hampshire, Nevada, Arizona
MID PRIMARIES (April)
Then have another 2 weeks of silence followed by 7-10 small/medium states spaced over 4 weeks with one large state mixed in.
March 27: Wyoming, Utah
April 7: Michigan
April 14: Mississippi
April 16: Florida, Alabama
April 24: West Virginia, Kentucky, D.C.
SUPER DUPER THURSDAY (Mid May)
Then have another 3 week gap, and in Mid May have Super Duper Thursday with 3-5 of major states, mixed in with about 5-7 others for a total of 10 states.
By that time 30 states will have voted in the race for their party's nomination and we will have likely had a nominee. The states will have been spaced out enough to allow movements and smaller campaign to produce results in states to allow them some attention from party faithful, decision makers and hopefully the media.
May 15: California, Oregon, Idaho, New York, Connecticut, New Jersey, Texas, Oklahoma, Louisiana
FINAL PRIMARIES (Mid-May to June)
Finish off May and June with the remaining 20 primaries, also grouped together spread out over 5-7 days.
An important component to making sure no state feels too left out is to rotate the states every cycle, primarily so no state is in June in back to back cycles, and every state is put in Feb to Mid-May at least once every three cycles. (Party rules that leave two spots for Iowa and New Hampshire could even be created).