Is it because they wanted to keep the party under the control of elites?

It was a bit of a compromise. It all goes back to the 1968 Democratic national convention. The short version is that due to declining poll numbers and challenges within his own party (largely over the Vietnam War), President Johnson chose not to seek his party's nomination for President, bowing out of the race in late March of that year. Three men were then competitive for the nomination: Senator Eugene McCarthy, Senator Robert Kennedy (the late president's younger brother), and Vice President Hubert Humphrey. McCarthy and Kennedy were both seen as anti-war or peace candidates, while Humphrey was largely regarded as coming from the establishment. Humphrey didn't think he had much of a chance in primary states, because the party in the electorate was largely anti-establishment (one of the reasons Johnson didn't run), so he worked on drumming up delegates from caucus states, where party leaders (and the establishment) exerted much more control.

On June 5th, Robert Kennedy was assassinated. At the moment of his death, the delegate count stood at Humphrey (561.5), McCarthy (258), and Kennedy (393.5). Kennedy's murder left his delegates uncommitted, meaning they could vote for whoever they wanted at the convention.

The 1968 Democratic National Convention took place in Chicago, and is really fascinating and deserves its own post. The long and the short of it is Humphrey ended up with the nomination, despite never having entered a primary (and thus never voted on directly by regular voters) and being from the establishment while, before Kennedy's assassination, the majority of delegates were pledged to anti-establishment candidates. Opponents of his nomination largely pointed towards Democratic Party heavy-weights such as Chicago mayor Richard Daley having had an unfair influence on how delegates voted. The Democrats lost the 1968 election to Nixon, and formed the McGovern-Fraser commission to attempt to fix the issues that led to the disaster that was the 1968 convetion.

The McGovern-Fraser commission was officially called the "Commission on Party Structure and Delegate Selection". They proposed a lot of changes, but of interest to us here is that they gave greater uniformity to delegate selection and voice to previously marginalized groups such as women, minorities, and young people. State conventions could also no longer select more than 10% of the total delegates from their state, and that state conventions could no longer designate ex officio delegates to the national convention. Other rules also pushed states away from caucuses and towards primaries.

In the early 80s, many Democrats felt like the McGovern-Fraser commission had gone too far in reducing the influence of party leaders, and that their changes had weakened the Presidential campaigns of McGovern in 1972, and Jimmy Carter in 1980. The Hunt Commission was established in 1981 to address this issue. Their solution was the creation of the superdelegate, a party leader not obligated or pledged to any candidate. Superdelegates have grown as a total percentage of the total number of delegates from around 15% to close to 20% today.

Were they trying to keep the party in the hands of elites? I'm afraid I don't know enough about the personal motivations of the individuals involved to answer that very well, but I think it was a compromise. One has to remember that parties are not necessarily a intrinsic part of our political system, and that parties are not legally (or maybe even morally) obligated to be completely democratic. For example, the Republicans do things very differently, and most small parties don't even have primaries and simply select delegates at state conventions.

Edited for clarity