If with 'cube theorist' you mean people like yourself, Lucas, Chris, Per, Cmwolla etc then I agree
They're all certainly theorists in the wider sense that they pose puzzle-theoretic questions and attempt to answer them, but not all of them use much that's actually theoretical, and I'm sure some don't know much group theory. To pick on Cmowla, he's much more of an experimentalist. Not that I have any problem with that in itself; doing often produces more useful things, and he's definitely done some cool stuff. But ad-hoc constructions and computations barely qualify as theory. More theory could help him become a more productive experimentalist, if only by pointing out provably fruitless paths of exploration....
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To clarify, almost any interesting exploration on the cube has to be more experimental than theoretical. I mean, the cube group is abstractly just a finite group whose structure can easily be written down explicitly; aside from its size, it's a relatively simple object. So it's to be expected that most mathematically natural questions about the abstract cube group are easy (e.g. order, commutator subgroup). The long-standing "theoretical" question of God's number was the explicit computation of some quantity related to this one Cayley graph, and relative to a set of generators that's pretty unnatural from a mathematical point of view (why include half turns?); the reason it was hard was because the thing is huge by the standard of today's computers, which meant that you had to be clever to make the computation feasible.
Most of the difficulty in cube theory comes from the fact that many questions we consider are only natural for the specific realization of the abstract cube group as a Rubik's Cube, and more specifically as a Rubik's Cube solved by a speedcuber. This means that many questions that are interesting for us are very unnatural mathematically. For example, one natural question for a speedcuber is whether it's possible to execute every PLL once and get back to the solved state. On the cube group, the subgroup P of elements that permute the last layer while preserving orientation is still a mathematically decent object (though you're already fixing a particular realization of the cube group rather than looking at it abstractly). But identifying different permutations as a single PLL by factoring out rotations and AUFs means (as you can convince yourself) looking not at P but at R\P/R, where R is subgroup of U turns. If you treat the cube as an abstract group, there's no good mathematical reason to look at these double cosets; P/R already fails to be a group, and there's no reason to expect much structure in R\P/R under the induced operation. Theoretical considerations may still somehow lead to a nice solution (more likely negative, if anything), but precisely because this question is mathematically unnatural, it's hard to solve it theoretically...which means we'll probably have to just compute. On the other hand, theoretical considerations may help simplify computation and make it feasible.
To summarize, many interesting problems for speedcubers are hard and more computational than theoretical because they're mathematically unnatural. There isn't much theory to know for cubing, say some group theory (say enough to fully understand the above) and some standard counting tools, and otherwise large computations will often be necessary. But knowing this much theory will help you organize and effectively carry out these computations. In other words, cube theorists are by nature be more experimentalist than theorist, but the best experimentalists are those well-versed in theory.
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In response to the thread, I think the key point is the difference between an abstract mathematical concept/object and its various realizations. Cubing (for 3x3) deals with one particular realization of one group that, abstractly, is mathematically relatively uninteresting. Rather, it is this realization and all its consequences (including consequences for cube theory described above) that make cubing interesting.
