I've heard that abolishing the electoral college is so popular with Democratic politicians and Democratic voters. I know the electoral college is different from how the Democrats choose their candidate for president, but I'm still wondering why they don't have one nation-wide primary for their presidential candidates and get rid the current system with delegates and a state-by-state process.
First, 'why' questions of this sort are misleading, and difficult to address directly. The system the Democrats use for their primaries has built up over generations; their original reasons and rationales for doing things as they do them are now buried in political culture and tradition. You might as well ask 'why' women still (to this day) take the last names of their husbands, or 'why' people in the UK drive on the left-hand side of the road. These are not things that are entirely subject to reason.
I will say that back in 1828 — when the Democratic Party was founded — a single nation-wide primary would have been impractical for a number of reasons, not the least of which is that candidates used the primary process to travel from location to location, making themselves known and drumming up support. Today we have instantaneous mass media that lets us watch candidates debate long before the first primary occurs; in 1828, we would not have known who the candidates were until our local paper picked up their candidacies, and we would have had no opportunity to see or hear them until they plowed into town before our state primary. And since the candidates can only make their presence felt in one state at a time — necessitating a long, drawn out process — there needed to be some method for aggregating and rationalizing the results of all these separate primaries at the end. That led to party conventions and delegates and the whole complex process of wheeling and dealing that we see today.
As to 'why' the modern parties don't adopt a more modern nation-wide plebiscite to choose candidates, given that we now have the technology to do so... There are several likely reasons for that:
- Party insiders do not want to give up their 'gatekeeper' status, which allows them to maintain control over candidate choice and party messaging. That may sound Machiavellian, but it serves a useful purpose of keeping the party focused on its platforms and goals. A national plebiscite could install a candidate who is deeply at odds with congresspeople and state governors from the party, which would create internal tensions and difficulties in passing legislation.
- States do not want to give up the particular power that having state primaries and delegates gives to them. In a national plebiscite all those tiny New England states and those underpopulated mid-western states would be washed away by monster states like California, Texas, and New York. At a convention, at least, a state like Rhode Island is guaranteed some say for its people.
- Candidates do not particularly want the process to be a simple public popularity contest. If a contest is close enough to produce a brokered convention, candidates can focus on delegates, and delegates are much more likely to make decisions based on a critical assessment of candidates' policies and potentials than an average citizen is.
And dare I say it, it's worth keeping in mind — particularly in the propaganda-driven, mindlessly reactive, hyper-partisan morass we currently call politics — that the public at large does not necessarily make the best collective decisions for itself. Democracy works well when certain sociological and psychological conditions are met — when we can rise to the level of what Aristotle called a 'polity': a collection of earnest, dedicated, 'virtuous' citizens — but as a society we are doing very little to meet those conditions, and certain elements within our society are actively trying to disrupt them. Unless we want Boaty McBoatface to be the next Democratic candidate for president, I'd be leery of a national plebiscite for the time being.
I would add another consideration to the list that @Ted Wrigley has offered, namely: Unity.
Either party (R or D) much prefer to put forth a candidate to the general election contest that has been selected by the majority of their voters.
Consider a national primary in which there are 10 candidates are running. It is more likely than not that none of the candidates would achieve a majority support in a national (one-day) primary. In that scenerio, the "winning" candidate would likely be a plurality winner rather than a majority winner.