Question is the title. Is there a real and cogent reason why each state’s primaries are on different days, weeks, months? Wouldn’t it be fairer and more straightforward (not that this is something that’s ever considered in American political structures) to just get it all over with on one specific date?
The only potential winners would be candidates that already have national name recognition. There would be no chance for any other candidates to raise money, build momentum, and get press.
Also, primaries are weird in that they are not “official” elections, even though they are generally conducted via the state voting machinery — they are a candidate selection process whose rules are (mostly) set by the parties as private organizations. In practice there are laws and regulations which govern aspects of their execution, but they remain kind of a hybrid procedure which is not fully owned by the election agency. As such the private state-level parties have independence and latitude to set their own schedules (in negotiation with the other state-level organizations and the national party), and there isn’t really a mechanism for imposing a date on them.
This.
Obama would never have been nominated if the primaries were all on the same date. He had to show voters in the later states that he could draw votes, including that he could draw votes in heavily-white states.
We should (in my opinion) keep the primaries more or less as they are, but what I would definitely change is I would break the states and voting territories into categories based on population and diversity and rural vs urban and so on, and then instead of New freaking Hampshire always going first I would lottery off from each category… but the first would never be California or Texas or New York, always one of the small ones akin to New Hampshire.
States also have an interest in standing out from one another. New Hampshire has been first for decades, and protects that position. Going first gets them extra attention from candidates, and gives them outsize influence on national politics.
The answer to the thread question is: History.
It used to be that a few states, perhaps ones that cared more about democracy, used a system of delegate selection — primaries — other than the norm of having delegates selected by politicians.
In theory, a party wants a system that gives nominees more likely to win. In practice, no one knows what that system would be. And the national committees have constituencies they want to please, while states try to maximize their power.
The Democratic Party has been trying for many years to get away from front-loading two states with a disproportionately white electorate. But New Hampshire has a we-go-first law. Iowa gets around that by having caucuses.
If all the states’ primaries were in early August, that’s plenty of time for fundraising, campaigning, and building name recognition. We don’t need to start the primary season in February.

n theory, a party wants a system that gives nominees more likely to win. In practice, no one knows what that system would be. And the national committees have constituencies they want to please, while states try to maximize their power.
Slight nit pick: I think that there are two competing interests in the candidate selection. One, as you pointed out, is which candidate is most likely to get elected, but the other is which candidates best represents the policy interests of the party. Balancing those often competing interests is what makes candidate selection such a tricky process.

If all the states’ primaries were in early August, that’s plenty of time for fundraising, campaigning, and building name recognition. We don’t need to start the primary season in February.
Timing of the primaries have changed over the years. But that doesn’t change the fact that it’s much easier for a low budget candidate to perform well in NH, Iowa, or some other relatively small state than to compete in a nationwide contest out of the gate.

Slight nit pick: I think that there are two competing interests in the candidate selection. One, as you pointed out, is which candidate is most likely to get elected, but the other is which candidates best represents the policy interests of the party. Balancing those often competing interests is what makes candidate selection such a tricky process.
The actual purpose of the primaries was to determine which candidate best represented your state’s concerns regarding national policy while representing the policy interests of the party as a more specific means of doing that. Since party has superseded state concerns in almost all states in each election the primaries are just part of the larger scam by the major political parties to subvert the democratic process. Of course no one really cares though, the system is traditional and we just insist that it works so we don’t have to face the challenge of improving it against the entrenched people who personally benefit from it at our expense.

If all the states’ primaries were in early August, that’s plenty of time for fundraising, campaigning, and building name recognition.
And it still doesn’t answer the point that Obama needed to prove to voters in later states that he could pull a significant number of votes in the earlier ones. That can only be done by holding some actual votes earlier than others.

The Democratic Party has been trying for many years to get away from front-loading two states with a disproportionately white electorate. But New Hampshire has a we-go-first law. Iowa gets around that by having caucuses.
I don’t recall the details exactly, this arrangement came about in the first place as a result of dissatisfaction with the “smoke filled rooms” or somesuch during the 1960s, probably McGovern? The Republicans played copy-cat.
Notably Jimmy Carter made effective use of the new arrangement of Iowa and New Hampshire. Various . . . refinements and other clever strategies were employed over the years. “Idiots Out Wandering Around” isn’t just a nickname. I think they are still counting from 2020

I don’t recall the details exactly, this arrangement came about in the first place as a result of dissatisfaction with the “smoke filled rooms” or somesuch during the 1960s, probably McGovern? The Republicans played copy-cat.
Think 1968, Chicago. Humphrey wins the nomination even though he didn’t win a single primary. The Republicans followed along because it vested more power in the parties while pretending to give the electorate more say.

If all the states’ primaries were in early August, that’s plenty of time for fundraising, campaigning, and building name recognition. We don’t need to start the primary season in February.
Then why did people start visiting Iowa and New Hampshire in early 2017?
At least in the Democratic Party under its current rules, a single presidential primary day would pretty much guarantee a brokered convention, unless you had some kind of pre-primary process that whittled the candidates down (but then you’re just reinventing the primary season under another name). Whether that would be “fairer” would depend on how representative you think the delegates are of the broader party that voted, I suppose. But that means you’d have to care about who the delegates are, which sounds like a lot of work.
How does delegate selection work these days? Seems like it used to be important to have delegates who were at least initially loyal to a candidate, in the old brokered convention days. As I vaguely recall, those would be recommended to a candidate’s campaign by state political organizations, which in turn would be drawing from local political groups. I think that’s how my father got to be one of RFK’s delegates from California. I’ll ask him.
and don’t forget 2020 when Trump tried to get alternate delegates in Ga.
jeez, can’t we?

Think 1968, Chicago. Humphrey wins the nomination even though he didn’t win a single primary.
Yeah, that makes sense. '68 was a CF year in oh so many ways. Johnson, who decided not to run, threw his support to Humphrey and urged everyone to vote for him. But everyone else was torqued.
So the “modern” system, including Iowa and New Hampshire and the rest of it, was soon gamed out strategery wise, notably by Jimmy Earl from Plains. I recall several co-workers who caucused in Iowa for Mrs. Clinton in the 2008 cycle were completely shell-shocked.