On the crimped primer pockets, you have the inner budge from swage crimping of the primer pockets, then there is the top of entry chamfer to allow the primer to enter the channel correctly as well.
If cases where chamfered, but not cleanly swaged all the way around inside, could be that one side still have the budge, and why the primers are trying to cant on you on the way in.
The cutter tools are not bad, so long as you hold the case to the cutter, and the tools like the RCBS with larger end stop work very well for small counts of prep.
As for larger prep work and still working off a single stage press to reload, then super swage 600 and other tool like it, are not that bad. The downside, these tools work off the web thickness of the case, so pretty much have to batch your brass to same manufacturers, then set the tools up for each batch of brass to swage the primer pockets. Hell, its the same for my 1050, that has the swager built into it.
Lastly, on some of the imported mil spec brass with crimped primers, primer pockets can be on the tighter side, and in some cases, the primer pocket depths on the shallower side as well. Most of us will just trash such off brass since it will take extra attention like use a primer pocket depth cutter to get it right.