I have three sets of tires and rims, 315x60x15 ET street radials, 13.50x30x15 ET Street(bias plys) and a set of 10.5x31x15W MT drag slicks, none of them have tubes or rim screws, the ET streets have moved about one inch in three years of running at the strip at 9.5 o 10.5 lbs pressure(1.50 60 ft. times, the radials are faster ) and 15 to 20 lbs on the street. the radials (18 PSI)have not moved at all, put a small dab of shoe polish or crayon on the tire and rim and watch for movement Not every car, tires and rims are the same so what works for me may not work the same for you

Like Cab, been running since 1964 and use tubes mainly to prevent leakage. Currently 14x32 Phoenix bias, but Goodyear, M&H, Hoosier, MT, even back to Casslers they all leaked even with the soap trick. Your results may vary.

On my previous tires, Hoosier 31-16.5 QTP's I ran tubes and screws. 16 screws per rim, 8 on inside bead, 8 on outside.
Here's an interesting deal. 15 of the 16 screws on the inside of the rims actually broke off. When I removed the screws, only the head and one thread was attached to the rim, the rest of the screw was broken off and stuck in the bead. None of the outside screws broke.

Current tire is a Phoenix Radial Slick, 32-13.6. No tubes or screws.
Put a dab of polish on each to check slip.
Maybe a half inch per side in 5 runs in vegas.
3 runs at Barona yeilded no more.
7 runs at Fontana, with 3 that really hooked good. One side moved maybe another half inch.
The other one moved 4 inchs or so. I'm thinking I'll go ahead and screw them down.

Better safe than sorry
What's the worse that can happen IF you run with screws

I have had tires turn/slip 3/4 of the way around in 4 runs if they had been freshly mounted and I had the pressure real low. Never caused a problem, but it can be kindof scary Only real problem is the tires go way out of balance. But I still don't like the screws and will not use them. I just mark them now when they are new and then SWAP them side to side to return the tire back to where it started mainly to rebalance the tire. Once they have been on the car for a while they stop moving. It's only because they soap them up when installing them, that causes them to slip. After a while they stick. After everything dries real good.

One of the old tire vendors at the National events siad to never tighten the rims screws all the way in, tighten them up and back them out 1/2 turn before running them on the car. That was with using #12 rim screws I have twisted them off when using a ratchet and socket and not paying attention I have also used the rim screws (6 or 8) on the inside only the choice is yours, I think the inflation pressure on the initial mounting and how long you leave them inflated at the higher pressures (25+ lbs overnight) make a difference on how they stick to the rim, maybe not