This is a subject with which I work professionally, so I can offer up a few ideas.
First of all, reform was inevitable. I'm on the road, so I don't have cites handy, but there is a great deal of academic and other work on the delegate selection process and the issues within the party that made some sort of nominating process reform a political imperative. Part of this was the decline in influence among the traditional party bosses that had theretofore controlled state delegations. However, let's assume that a similar set of reforms happen, but it gets delayed by, say, a decade.
The two most obvious outcomes here are that you've eliminated McGovern and Carter as nominees as both won nomination under the new system as relatively unknown insurgents. Who benefits? Probably Hubert Humphrey or Edward Muskie in 1972; Ted Kennedy was still too close to Chappaquiddick. Assuming either one of them loses to Nixon as McGovern did, that leaves a lot of interesting possibilities for 1976. OTL, 1976 had a whole lot of candidates. My guess would be that the nomination would go to someone with close ties to labor who's pretty much in the middle of the party. Maybe in 1976 Kennedy could get support, maybe not. That one's really hard to assess. In 1976, you had a lot of interesting candidates in the field running the gamut from Scoop Jackson on the right to Mo Udall on the left, with some other candidates like Birch Bayh thrown in for good measure. Here's a list:
http://en.wikipedia.org/wiki/Democratic_Party_presidential_primaries,_1976
Two of those who dropped out before the primaries began, Mondale and Sanford, might have had some appeal to party leaders under the old system.
However, I think that by 1980 there would have been reform; perhaps even as soon as the aftermath of what would probably have been another lopsided loss to Nixon. Nothing gives reform as much of an impetus as losing elections. It's very possible that you'd have a 1976 nominating process under new rules not unlike what McGovern/Fraser came up with. In that instance, assuming Watergate occurs much as it did in OTL, you might have a McGovern '76 campaign. Unlike 1972, that's a race he'd have a good shot at winning in the fall.