Run 'n Gun has held very little success for me over the years. I don't practice it much, but I'm not going to knock it.
I'm hunting a single 200 acre parcel. I have gotten so I have certain set spots. If the turkeys are active in spot A, I go hunt A. If that doesn't pan out, I try and get up and go try B or C. By then, it's time to go in have coffee and start glassing for them out in the pastures. By the time I hang up the shotgun and start thinking about declaring Happy Hour, I may have gotten up to L, M, N, and spent half the afternoon lurking at O with a good book until I was sure the birds were going to roost. It isn't Run 'n Gun, but I won't say I sit tight in one spot dawn to dusk either. The trick is that I try and make my moves for some reason. It may not be much of a reason, in fact it may just be a wild hunch, but over time I figure that the gobblers and I are going to meet up.
Now I can see if you're hunting large tracts, public lands and so on that running and gunning might have appeal. If you look at it as armed scouting, you can cover a lot of ground in one outing. It's just that if I did much of it, I'd go a half mile or so at most and be to the end of my property. The one time of year where I could conceivably be on the move more is that period of the season where lone gobblers are trolling about and gobbling down every little hollow looking for a midday hookup. That is a behavior I've seen, but not too often. Usually the season is in its last stages before I see it, or I find them doing that right after season. Even then, I try to get out and scout ahead of those times and pattern the gobbler; I've seen them take the same track 2-3 days in a row, making a circuit of a mile or more 2-3 times in a day. I try to be in a good spot to hook up with them, and then just wait for the gob to circle on past. On those days, gobblers will come almost at a dead run from 300 yards out if they hear a hen yelping.