Two untrained people fighting will likely result in a ground scuffle. My Dad was an experienced "club fighter" from the 60's and a brawler by anyones definition, he always told me the fight completely changes when you go to the ground. Try to avoid but it is going to happen. We do train in specific ground fighting techniques in our dojo and think it very valuable training for any Aikido player.
Fights end up on the ground a LOT. But fighters are not taking the fight to the ground intentionally. Fighting folks fall down, and they usually have as little of a clue about what to do on the ground as they have in the standup portion of their fight. A little ground skill goes a long way, I could use a bit more instruction in ground fighting.
I've noticed 3 stages in most of the fights I've witnessed and broken up. 3 Fs - Fussing, Fighting, and Fucking. Two are good points for intervention, from a fight-stopper's point of view. If the people are jawing back and forth, get in quick, separate them, calm them down and either bounce them or throw them back in if they calm down well and agree to behave. If they're already shoving or punching, wait a minute, you may get hurt intervening. They'll pretty quickly get to the last phase, clinched and rolling around on the ground like lovemonkeys. Much easier place to dogpile yourself and a few coworkers on them to get them separated, restrained and hauled the hell out.