Smokin'Joe:
Now THAT'S what I'm talking about, a new idea! Time will tell if it's the best one (we engineers know that there's always a better idea), but at least it makes some sense.
FotoJoe:
Tapers work, when the materials have elasticity. Caps don't; they are made from annealed copper or brass.
beag_nut, I can assure you that caps have elasticity (or at least "enough"). I'm going to use some terms like "usually" and "probably", but caps are going to usually be made of a high-copper alloy, probably either C21000 or C22000. (Unfortunately, I do not know the exact alloys used by various manufacturers.)
About the taper design being inferior and the caps lacking elasticity... For example, CCI #10's are too small for my particular nipples. The skirt on the cap makes a solid contact with the outside taper of the nipple long before the priming compound in the cap can get close enough to the face of the nipple. I'm literally doing this as I am completing this message. Using only moderate thumb pressure, the cap is so firmly seated on the nipple that I can't remove it, even with the cylinder removed so I can get two fingers on the cap. I'm either going to need pliers, or to re-mount the cylinder to my frame and fire it. Because the cap is tight, but the priming compound is not fully seated, it may take 2 or more hammer blows before it will go off. Again, my case is obviously different. These caps are too small, while CCI#11's are slightly oversized, and require pinching on my particular nipples.
If none of the common brands/sized of caps will fit your nipples, they might:
1) Have the correct taper angle and nipple length, but were cut down to an undersized diameter.
2) Have the correct taper but the nipple was not cut short enough (too long).
3) Have an incorrect taper that is too shallow.
In all 3 cases, the cap would bottom out before its skirt had a chance to grip the taper.
If pinching or otherwise resizing your caps is unacceptable, and unless the cause happened to be 2), I would say a new set of nipples. There are several "if"s involved for remedying #2, but buying new nipples is still probably the preferred solution to that as well.
I think makos_goods(?) posted some nice CAD models to illustrate cap fitment and the relative sizes of various cap brands. If I can find it, or someone else does, I think they may help you visualize what is really happening.
Edited to add: I did manage to remove the cap, and a piece of my thumbnail, without aid of hand tools. YMMV