> It's up to each party to set the rules on how delegates can be selected, including time, place, and manner.
It seems that Iowa chose both, the time and the manner, itself[1]:
> Because Iowa had a complex process of precinct caucuses, county conventions, district conventions, and a state convention, they chose to start early. In 1972, Iowa was the first state to hold its Democratic caucus, and it had the first Republican caucus four years later.
> Under Iowa law, political parties are required to hold caucuses every two years to select delegates to county conventions and party committees.
And each party must respect the laws of the state.
> It seems that Iowa chose both, the time and the manner, itself
Well, no, not entirely. Yes, the parties gave them lots of room initially, but that has evolved. The entire reason they were using the app at issue this year is because after complaints about apparent inconsistencies in the results based on internal reports (there was previously no official tally of the intermediate steps), the DNC directed that to the Iowa Democratic Party must adapt the method so that there were official, reported tallies of the first and second alignments as well as the state delegate equivalent count that is the final result. That is, the national party chose (in a very limited way, for now) to exercise it's fairly absolute power to direct the manner by which delegates to it's nominating conventions are selected. (Aside from this specific intervention, the DNC also has extensive general rules adopted for the delegate selection process, see, for 2020, generally Regulation 4 of the Regulations of the Rules and Bylaws Committee for the 2020 Democratic National Convention.
There is nothing stopping the DNC from making much more exacting requirements, including setting a required schedule or prohibiting the use of caucuses entirely.
> And each party must respect the laws of the state.
Each party has an incentive to do so to avoid conflict with interest groups in the state, but state governments have basically no compulsory power to direct how party national committees allow delegates to nominating conventions to be selected from their state.
As I understand, it's up to each state to select the date.