The word “brokered” emphasizes the “power brokers”, the people who used to sit in smoke-filled rooms who decided who’d run in the era before the modern primary system. That’s rightfully seen as a bit undemocratic, so they’re held in reserve for the rare times when the democratic first ballot fails and the party needs some method beyond “who got the most votes in the primary season” to pick a candidate.
Apparently, people don’t like the idea of power brokers or smoke-filled rooms or anything like that, so they say “contested convention”, possibly to emphasize that the candidates will be contesting the results after the usual stopping point. That, and modern parties abandoned the “Boss” and “Ward Heeler” system along with the old Machines, which makes it something of an open question as to who these power brokers would even be at this point.
Side note: This is one of the things superdelegates are good for, in fact: If Candidate A has almost enough and Candidate B has a lot fewer but still wants to run their campaign down to the wire, the superdelegates can support Candidate A, put them over the top, and avoid any messiness at the convention. (Or, well, avoid the worst messiness. Candidate B supporters are guaranteed to grumble about superdelegates, but the rest of the party can remind them that the rules haven’t changed and that avoiding floor fights is important, too.)