Supersymmetry solves two well known problems, one of which is a bit of clutter [the statistics problem] and the other is serious, the so-called hierarchy problem.
The statistics problem does not seem to be a big issue to me. In fact, I would call it a non-issue. [It would be interesting to have some real physicists weigh in.]
Classical particles are not fermions. But they are also not bosons, and the "correspondence principle" still heavily leaned on in many basic physics texts as a note-added-in-proof is not taken all that seriously by most physicists anymore.
We see non-classical behavior in "large" systems, and we see non-classical behavior in statistical mechanics at all temperatures and in large ensembles as well, and that's just all there is to it.
In fact, I would guess most physicists these days would take the opposite conceptual approach and say, "well, if quantum physics appears to reduce to classical physics in some scenarios, that's great. But it doesn't mean anything conceptually. You just have to account for why classical physics is a good approximation in some cases, without expecting that to always be true, even in the everyday world."
A great example of that is the behavior of metals. I got into an extended dust-up a number of years ago with a FReeper who called himself RightwingProfessor [who got himself banned for his nastiness on the Crevo Threads.] He maintained that you really don't need quantum mechanics "except in situations that never arise in ordinary life." This is complete baloney. It's impossible to explain the properties of either metals or semiconductors without Band Theory, which relies very heavily on Fermi-Dirac statistics, which in turn is completely unexplainable without a hallmark of quantum physics: indistinguishability. I don't think any practicing physicist today would claim that we have to find a way to reduce Band Theory to Newtonian physics to convince people that it works. [Another great example: lasers; which can't possibly be created in Newton's World. Thank God we don't live there.]
The hierarchy problem, on the other hand, is a serious issue. Basically it boils down to: "we don't understand why the weak force is so much stronger than gravity." That is a problem, but there are alternative explanations for it that don't require supersymmetry. So it is not an intrinsic weakness in the Standard Model. Extra dimensions is a known dodge, which might turn out to be correct if Supersymmetry isn't.
There are also some other things that Supersymmetry neatly explains. That's not surprising. Some very smart people -- a lot smarter than me -- have been working on it for a really long time. IIRC, something like, 60 years. But there are some alternatives which also explain, or take a stab at explaining these things without abandoning the Standard Model as well...
We shall see.
It’s obvious to me you know a heck of a lot more about this stuff than I do. I always appreciate your comments, and even if I don’t always fully understand them, I’m sure to learn something substantive from them, thanks!
God should really come down from on high and explain His creation once and for all.