The small base dies also narrow the case more. There seem to be some chambers, particularly tight match chambers, that require these dies be used in order to feed properly. That is unlikely to be an issue in the Mini-14. Also, range foundlings and once-fired brass often are long enough that you need to use a small base die the first time you size them to get them small enough to feed.
Personally, I've seen so many problems with once-fired brass that I won't buy it. I've got a bag of 50 .223 military cases a fellow sent me that could not be sized to chamber no matter what he did. Upon measuring them for him, I found some with shoulders already pushed back as much as 8 thousandths below minimum, but that were still too wide near the pressure ring to chamber. In some instances they had bent rims that accounted for much of the problem.
There have also been two threads I've followed in as many months in which once-fired cases caused sticky extraction pressure signs with very modest loads. These were cases that were apparently stretched so severely that the brass was not responding normally to pressure. I didn't get to examine them, but in one instance I actually sent five new Lake City and IMI cases to the fellow having the problem so he could prove it didn't happen with good condition military brass. This was a .308, and where 40-41 grains of powder was a normal load with the new brass, his once-fired cases had to be loaded with no more than 34 grains to avoid sticking in the chamber. I'd have tossed it, but he's going to use it for reduced loads.
I prefer to suck up the cost of new brass and not have to deal with oversize or overstretched cases in the first place. These almost never require a small base die to be returned to a fit in the same chamber.
The X-dies apparently work as advertised. For progressive loading, they should be a good idea, but they don't get you out of removing the sizing lube, which you don't want getting into your chamber. So, be prepared for a short tumble in plain corncob at the end. There are warnings against tumbling loaded rounds, but a number of independent experiments indicate it doesn't cause a problem. These have including tumbling for many days. I am guessing that the graphite on most powder lubricates it well enough so it doesn't wear easily in these situations, but some modern powders don't use graphite, and I would be wary of extended vibratory tumbling with them until it can be shown it doesn't affect them. A short run of 15 minutes or so to clean off lube should be OK. They get that much shaking up in transport anyway.
I don't like using solvent to remove lube from loaded rounds, as the primer is vulnerable to wicking it in. However, a rag moistened, but not flooded, with mineral spirits or even water (for Lee's case lube) should be possible to wipe off the surface with without touching the head or primer pocket lip.