Well, the problem is that it's often difficult to get a large number of practitioners together at a specific place and time.
On my side, me and my group of amateurs haven't had much experience with group sparring since we can't even be guaranteed to get the individual techniques right. But I guess I'm allowed to digress and say something about the weird old days when I got drafted into a community watch program, which included riot squad training with batons and rattan shields--and part of the training involved building our aggressiveness by lining the people up in two opposing formations of around forty men each and having us charge against each other. At first we were a bit shy, and ended up stopping just within baton's reach and poking at each other while hiding behind our shields. But it was a session meant for building aggressiveness after all, and by the end of it the instructors succeeded in having us line four deep and really charge into a shield-to-shield shoving match. One hell of a shoving match, that was. The collective shield push became our primary weapon and we used our batons only as weapons of opportunity--taking potshots at exposed heads and shoulders. We had little room for technique (of which we were only taught a few anyway). Victory was just a matter of who had the more solid formation, better morale, and pushed harder.
Definitely some different mechanics from one-on-one or even few-on-few!
That was before I got involved in WMA. If any of us had known the German masters back then, maybe he would have urged the rest of us into the shove in the first place--before our opponents were ready for it.