I have worked in all kinds of settings, classical orchestras, Big band Jazz groups, small groups, etc. I think that for a small group being in the pocket or holding a groove is an easier thing to do, at least in theory. The players can see each other, and there is a degree of "conducting" going. I used to sit in front of the rhythm section in a big band in college and the drummer could accent my solos in the just the right place without any rehearsals (and they were different every time). He said to it was easy because I was telegraphing what I was going to do with my body language.
This is hard to do in a 100+ person orchestra and a conductor is needed. There is no reason for an orchestra to be sloppy with time. But I think it is the conductor who is driving. With enough practice all the team members should have a "feel" for what's coming but they have to be open to following the conductor.
I have never heard an orchestra keep the beat poorly, this is a basic element of music. But there some grooves that are very laid back. An example is the en clave' Latin groove. As it was described to me it's a grouping of 5 beats but cannot be strictly counted like 5/4 time. The placement of clicks is so loose that you have to feel the entire measure and any attempt of quantify it in terms of fractions of a beat will lose the groove. I think really heavy delayed back beats in greasy funk follow a similar patter. Everyone needs to know it, feel it, and it likely works better in a small (or small-ish) group (Parliament was a large band but not a 100+ orchestra).
In my experience when very large orchestras play modern pieces they tend to lose the groove and acquire a more tight march-like feel, imo due to everyone following the leader's beat rather than "feeling it". But I do not think it's impossible for an orchestra to generate a greasy groove. That would be very impressive.
In terms of "crowd wisdom" I am not sure what you mean but every musician should have an internal metronome. That's part of the training. I had conductor who would famously start every practice with "Everybody here counts, some more that others...". But everyone must count together.