It's worth noting that 520.53(k) is relatively new, having appeared sometime in the last 15 years. For the most part, people were already using cam-locks by that point, as tweco's were already outlawed as unsafe in most jurisdictions.
The newer single conductor cables (type G and W) didn't start appearing until about 15 years ago, prior to which welding cable was the de-facto standard. I have not heard any reports of problems with the use of welding cable, other than the fact that the AHJ's in some areas didn't like it. In some areas, there is still a lot of welding cable in use, simply because of the large inventory already in service. The main reason that welding cable was banned was the lack of a double jacket.

The other popular cables are 2/4 and 2/5 SO, either with cam-locks, or one of several types of pin-and-sleeve type connectors.
Some folks use 6/4 with 50amp 120/250v twistlocks.

I will note that the code limits the number of mated connector pairs in any cable run so as to effectively require the use of 100' sections of cable. We commonly ignore that requirement, due to the inability of a single stagehand to carry a 100' section of 2/5 SO or 4/0 type W by himself. (I can and do carry 50' sections by myself when needed. It's heavy, but it can be done, and I'm 5'11 130lbs... the cable weighs almost as much as I do.)

Every cam-lock rig I've seen had the phases on females on the line side. Some systems reverse the ground and/or neutral to prevent mixing them up, but I prefer to have them all the same direction.. It's no fun having to pull one or two cables out of a run, and re-run them so that the connectors match up, just because the grunts pulling the wire were not paying attention, or didn't know what config the rig was in. (which may not have even come off the truck yet.)
So, you end up carrying gender benders, but of course, you never have enough of the correct ones when you need them, or you find that the local crew snagged some at the last stop on the tour.
Thats why most rigs will carry their own feeder cable, with tails, so that all they need is bare lugs to tie into.

Our generator vendor provides motion-picture grade (quiet, crystal synced) gensets, and ground and neutral are tied together inside the generator.

We seldom drive a ground rod, since a lot of our use is on concrete, where there is no place available to drive it, and the generator ends up being completely isolated from ground.

Inside, I use the house ground if it is clean, but sometimes we end up grounding to a cold water pipe (standpipe is preferred). Modern dimmers are much better than they used to be, bit some of the old ones could send a lot of hash back on to the power feed.

I've also done shows where we would bring in a portable transformer, and take a 480v feed from the house, and drop it to 120/208 for our rig.

For onstage distro, you see a lot of L21-30 and L21-20 5 wire stringers, with individual circuits broken out every 5-10 feet, or L14-30 and L14-20 4 wire, and L5-20 and L5-30 single circuit cables.