I had my first lesson on seater plugs with a Lee RGB 270 seating die and 150gr Nosler partiton seconds which had irregular lead tips, the hole in the seater plug was too small for the tip of the bullets, so it didn't center the bullet by pressing on the ogive, instead it would hang up on the lead tip and not be centered consistently, was easily solved by drilling the hole larger to press on the copper jacketed ogive instead. Flat point seater dies like the Lee 357mag aren't so easy tho, there is no hole, just a concave surface which as you mentioned, doesn't work worth beans on a spitzer bullet, not even a flat point like the 180gr Speer which I was loading. I also recently learned the Hornady New Dimension 260 Rem seater plug won't work on VLD bullets, it's too shallow and the long narrow point hits the end of hole in the plug before the ogive touches. I just bought a Hornady concentricity tool which also can remove bullet runout, I ran some Remington 260 factory ammo thru it, all but one rounds measure .002"'.003" runout, but one had .006", that would more that likely been a real flyer had I not corrected it.
Tim