For what is worth, here are my loose thoughts on some aspects of this discussion. This probably won't bring anything new, but hopefully will strengthen some opinions:
1. I agree with Evan that position tolerance can be used in case of tapered features, even when the feature is non-uniformly tapered. Such feature, if fully defined for its size and form (through profile of surface tolerance), falls under definition 1.3.32(b) - irregular feature of size type B - where the shape of the envelope contained within this feature is simply "other than a sphere, cylinder, or pair of parallel planes". I am not saying this is the best approach to tolerance such features, I am just trying to say that this technique is valid and mathematically interpretable.
2. Assuming that only the profile of a line / position combination is applied to this fancy-shaped hole, this is not legal callout. Profile of a line itself is not capable of controlling size and form of the feature depth-wise. Thus, even without going into details on whether it applies to specific single slice or to multiple slices of the feature independently, this combined callout violates one of the fundamental rules of dimensioning and tolerancing as defined in para. 1.4(b) - not every characteristic of the feature is fully defined. The deck of cards example is absolutely spot-on.
3. Like it was said, by default profile of a line callout applies to the entire depth of the feature, unless otherwise specified. Therefore, if the intent is to apply the profile of a line requirement just to a single slice or to restricted depth of the feature, it must be clearly stated on the drawing. And by analogy the same applies to the position callout. But even if it is done, the rest of the feature must be somehow controlled in order to avoid incomplete definition of feature's geometry.