Sorry to disappoint all the political junkies who pray every night that they will one day get to see a brokered convention, but such a scenario would be an absolute disaster for the party. Can't find the link, but I think it was Ed Kilgore who wrote a piece in 2016 explaining how such a convention would actually work from a logistical point of view. Basically, it would take what has traditionally been a four-day infomercial and turn it into a divisive spectacle with no one really in charge and inevitable bruised feelings once a winner was declared.I think you are right if the Presidential nominee gets to choose his or her running mate. But @KiddLattimer specified that the ticket would be from a "split convention." In that scenario, the nominee might have to team up with one of the other candidates with a bunch of delegates just to get the nomination in the first place.
What that means is this: Once a plurality leader emerges, there will be tremendous pressure for everyone to get on board with that person. Let's say you're a moderate who's incredibly skeptical of Bernie's chances. In what might otherwise be a 50/50 election, you think Bernie only has a 35% chance to win. But if you support a contested convention, with the goal of wresting the nomination away from him and giving it to Biden or Bloomberg, you're going to royally tick off all the Bernie supporters, and ensure that the eventual nominee's chances are way south of 35%.
Trump 2016 offers a perfect example. Lots of GOP power brokers assumed he was a goner. But they also recognized he was still their best bet relative to some cockamamie plot to unbind the delegates and engineer a Ted Cruz nomination. And they were right.
What's more, such a scenario is even less likely this year, when the entire party recognizes that the country faces an existential threat in Trump (even moreso than in 2016, when Trump was seen as a sure loser). The pressure to unify well in advance of the convention will be overwhelming.