No doubt that a neck has to be straight to minimize bullet run out. A crooked neck leads to a crooked bullet. Before I got the fancy dies, I used plain RCBS dies. I loosened up the expander ball shaft so that it "floated". This was so the neck did not get pulled one or another. It helped, I never tried to expand in a separate down stroke step, it might work.
I also have both RCBS and Hornady bullet run out gauges. The jury is still out as to which one I like best. One can show little run out and the other will be out - they do not correlate. I like the RCBS, but I have issues trying to keep the bullet into the bottom of the "V,s" consistently. The jury is still out on the Hornady yet, I just have not used it enough to say one way or the other. I made a home made bullet run out gauge. I made two "Vs" out of sheet metal bent over the ends and mounted them on a piece of wood. I then drilled two holes spaced a little further apart than the case, about mid way between the Vs. I ran a string up through one hole wrapped it around the case and back down the other hole. I could then spin the case and watch the bullet tip. I could vary the speed of the spin, by how fast I tugged the string on one side. I could not measure how much run out I had, but if it was very bad more than .003" or so, I could detect it wobbling if spun fast enough. I could then make adjustments to my loading techniques to remedy the situation.
I also agree the lots of neck tension leads to crooked bullets. I have had bullets that you could pull out with your fingers that shot lights out. Problem was they had to be handled with extreme care so they did not fall apart before you pulled the trigger. They have to just have enough tension to hold them into place reliably. Reliability depends on the application too. If I were on a life time hunt where reliability is a must, I would use a bullet crimp. For the bench or PD fields - no crimp and as light of tension as I can get by with reliably, .001" is enough.
Good Shooting and Good Luck