There actually is no legal reason why presidential primaries couldn't be held on the same day. There are, however, any number of political and logistical reasons why such a move would be counter-intuitive for both major political parties. While the Constitution does specifically mandate a single day for presidential elections, there are no federal provisions for individual primaries. States have the right to determine their own dates for presidential primaries, or even the right to hold caucuses or other political party conventions instead.
One reason holding all presidential primaries on a single day would be problematic is logistics. Candidates from both parties would not be able to campaign in all fifty states effectively before having their political futures determined on a single day. If all of the states, large or small, held primaries on the same day, candidates might concentrate their efforts on only the states with the highest populations or the most political influence. Voters in smaller states would be asked to select a candidate with little to no chance to examine his or her stance on the issues.
There is also political momentum to consider. When smaller states hold early presidential primaries, the results of the voting can either improve or hamper a candidate's overall momentum towards his or her party's nomination. Staggering the primaries over several months allows candidates to gauge their relative popularity and adjust their focus on future campaigning efforts. Candidates can also determine whether to continue pursuing their party's nomination or drop out of the race entirely. If all primaries were held on the same day, some promising candidates would not have the opportunity to build up more support. Only the front-runners at the time of the primaries would be likely to receive their party's nomination.
The Republican and Democratic parties of each state have the right to choose the day of their state's presidential primary. Many states believe it is to their advantage to hold presidential primaries early, since late primaries often have little bearing on the eventual outcome. Several states do hold primaries on the same day, usually with the designation "Super Tuesday." This decision to hold simultaneous primaries is often the result of consultations between the national political parties and individual state party representatives.
While it would be technically possible to hold presidential primaries on the same day, it would not make much sense politically for either party. The primaries are not the same as presidential elections. Primaries generally guide political parties towards a nomination of their most electable or popular candidate. Conceivably, an early front-runner could become less popular as the campaign season wears on, so a staggered system of primaries can reveal the candidate with the most momentum and staying power at the end, not necessarily at the start of the race.