#1 Runout isn't an issue that's corrected by a sizing die, more on that later. I mean brass moving in terms of FL+mandrel might move the brass -.005 then +0.004 to get to a net -.001. A bushing and mandrel you could do -.0015 and +.0005 to get to the same -.001 point. The total distance the brass moves does have an impact on the case by work hardening the neck. Which leads to the the second point of:
#2 I'm meaning spring back here to describe how case hardness increases when being worked, and over time the case will spring back more no matter how long you hold it in the die or how tight the die is. Hardening can be accelerated by moving brass more than necessary, holding down longer won't change the dimensions of the fired case versus the inside of the die. An FL die can't be adjusted smaller as brass hardens and springs back more, resulting in less neck tension/interference fit/hoop tension (or whatever the popular semantic term is today) when you seat the bullet.
More ADHD thoughts, the "you" here is the indefinite, generic muse that my brain talks to itself with:
Runout can be managed in a lot of ways. If you're having runout problems then you should take a holistic look at your complete reloading process, including components. FL+button, FL+mandrel, bushing+button, bushing+mandrel, LCD, separate bump and neck dies, all of these should be able to produce low run out loaded rounds. All the combinations should work because there's a point where the die stops mattering in that it doesn't induce runout, but it won't correct for runout being induced elsewhere. Bullet seating is an important part of the process - the straightest brass around can be pushed out of true by a low quality seating die, and also by the combination of sizing and bullet fit. My experience tells me that shoving a flat base bullet into a very tightly sized, very hard neck with a generic seating will induce more run out than sliding a boat tail into a minimally sized, annealed neck using a chamber seating die. So which parts of the statement matters most? Bullet base, seating die, seating stem, neck die, neck size, neck hardness? I don't know, because there's no one right answer, just finding the right balance and process that works for you and your rifle. Controlling what I can to reduce the height of multiple tolerances in the stack is IMO more important than making any single tolerance nil at the expense of making another taller.
There's also a flip side issue to #2 up there that even as necks harden a standard minimum spec FL die might still be undersizing the neck, and the bullet seating operation will do double duty of seating and the final expansion of the neck, which can lead to inconsistencies in seating depth and more runout. A bushing die you can put in a smaller bushing and end up with more consistent final neck ID as the case hardens over its life cycle - if you don't anneal.
If you do anneal, you can get consistent results in other ways, including an FL die. That was the point about you can get there in a lot of ways, dies aren't the only part of the equation. If you FL size and anneal, there's a very real chance you never split a case neck before you lose the primer pocket. If an FL die is giving you the accuracy and precision you want, there wouldn't be a benefit to changing to a bushing/mandrel set up - cost/benefit return would be nothing because you get no benefit since you got no change. Now if you're looking for more precision than you're getting currently, the tuning options of a bushing/mandrel might be worth the cost because it's a way to see the impact of neck tension/et al adjustments on a target. But if you're not to where you'd see results of the change in ammo quality because you're doing one of many other things - using recycled brass, cheap bullets, a crappy chamber, a poorly stocked rifle, back to no benefit. You'll never see the results of changing your sizing process on paper unless it's the limiting factor of your loading AND shooting currently. Which takes me full circle back to runout. If runout is causing issues on the target for you, the sizing die isn't where to start IMO. A blank drawing board is, otherwise you might be shotgunning money at the problem trying new sizing dies instead of actually finding your true root problem elsewhere.
