I think side lugs are mostly for show. I had some Swampers on my rig once and could regularly feel the lugs clipping the rock shelves without any noticeable effect on traction.
I agree that side lugs are mostly for show.
I don't have rock crawling experience, but I've done everything else in my younger days. I try to keep the adventures milder now that I'm old enough to know better, but I still have some fun.
I agree that IME side lugs are mostly for show in regard to mud. I'll defer to others regarding rocks.
For sand they are a detriment, IMO.
For anything else they're just for show.
They make it harder to fit big tires without rubbing sway bar or LCAs.
Also, large side lugs add weight, which I think is more fat than muscle.
When I buy tires, one of the things I prefer is small, modest side lugs. No side lugs is OK too.
My Cooper AT3 have no side lugs and they're way better in mud than BFG AT which has some side lugs.
The only situation I've seen side lugs help is when you fall into ruts and then you're trying to climb back out of the ruts. Like muddy ruts for example. In that situation, big side lugs can help you climb out of muddy ruts.
But without big side lugs I can fit a larger tire, which means it doesn't matter as much if I fall into ruts.
So that keeps me not wanting big side lugs. I think they are as much a detriment as a help for all purpose, all terrain wheeling, especially on a daily driver.
BTW - speaking of daily drivers, I think big side lugs make a lot of wind noise at highway speeds.