If nothing better comes along....
TLDR: Consider a flare.
I also have no love for a straight cut, but that is all there is for progressive rigs.
I run the vast majority of my loading in large batches on progressive loaders, not everything but most of it. By no means should what I am about to say be interpreted as the way I do all my loading, but not all loading is the same so this suggestion is not for everyone or all types of loading.
When faced with bucket loads of prairie dog ammo to be done, I wasn't about to run them all by hand through a Giraud or Henderson, nor am I typically going to hand feed them over chamfer tools in all situations.
An alternative that I found to be easy enough, is to slightly flare the case mouths in the similar fashion as pistol ammo. It works just as well on bottleneck cases when done carefully.
You can buy a Lee universal flare die or you can make your own tools. I have made my own for 204 and 17 cal.
The flare does two things. It turns that kerf angle of the sharp edge just enough to prevent it from cutting/scratching the jacket, and it also dulls that edge.
I must mention another detail here about my processing order since I multi-stage the processing on the Dillon 750 or 1050.
When that trim die is sizing the necks, the case is lubed. When that stage is done, the cases are tumbled to remove the lube and this step also helps dull that edge and also removes any swarf. My flare occurs later during the loading stage.
The seating step is followed with a taper crimp to insure there isn't any flare left after seating, but to be honest the flare is small enough that there is little of it after seating in most instances and the taper crimp is only to ensure the case mouth is straightened.
With boat tail bullets, the flare prevents the sharp edge of the straight cut from scratching the bullet, and it even makes the bullet placement easier for the bullet feeder or your hands. I don't run giant batches of flat base bullets, so no comment on how those would run but my guess is this would make them much easier to place/start as well.
I do sometimes prefer to hand run 223 cases over motorized chamfer tools just before the tumble step, but I must explain why. The reason is that a chamfer tool can "detect" split necks. Not all brass does this, but 223 AR brass does it much more than bolt gun brass.
There is a distinct "clicking" that is felt when a neck is about to crack or has started to crack as the cutting edges of the chamfer tool work the neck. This begins to happen statistically after several cycles but before the whole batch gets retired. I can catch about five to seven cases per thousand at this step, and that is after rejecting some before even getting started. So for me, manual chamfering is worth that screen, and then I usually still flare them.
So, consider the flare option when running the straight cut. Just food for thought until someone invents a better mouse trap. YMMV