Is SUSY really the only known approach to "merge"/unify bosons and fermions in a common framework?
BONUS question: If SUSY does exist at high energy, it seems unnatural and "not simple" in the sense it could imply a non-minimal model (or at least a very special MSSM from the current LHC data). Are these "facts" good or bad things for both theory and phenomenology?
If by unification, one means that the bosons' and fermions' properties are linked to each other by a principle, the answer according to everything we know is Yes because the only principle able to link properties is a symmetry and a symmetry mapping bosons to fermions and vice versa is clearly a Grassmann-odd generator which has to carry a half-integral spin by the spin-statistics theorem – and we just call all the possible choices "supersymmetry".
It is not true at all that supersymmetry requires a "non-minimal" model. Supersymmetry is a symmetry and models constrained by an extra symmetry should be viewed as "more minimal" than the unconstrained ones. Once this principle – supersymmetry – is imposed, the possible theories are still non-unique. But among them, one again finds some model that is minimal – MSSM stands for the Minimal Supersymmetric Standard Model. Whether or not the total "number of fields" is greater than in the Standard Model has nothing to do with the minimality. The fields are coming in supermultiplets and are required by the symmetry so they're not independent and one mustn't count them as "steps away from the minimality".
It is not true at all that the MSSM is ruled out by the LHC data. It is not even true that the viable corners of the MSSM have universally heavy superpartners. A notable example is the regime which may already be collecting evidence from the direct dark matter searches in which the LSP, the dark matter particle, is a neutralino lighter than 10 GeV (mostly bino/photino) and the next-to-lightest particle is the sbottom around 20 GeV, see
http://www.quantumdiaries.org/2013/09/20/zooming-in-on-new-particles/
http://motls.blogspot.com/2013/08/both-neutralino-sbottom-may-weigh-below.html?m=1
This region of the MSSM parameter space is compatible with all the LHC data and its possible advantage over the Standard Model could soon get inflated. There are other regions of the MSSM that are doing perfectly fine. Of course, Nature may choose a non-minimal model, too. The NMSSM is favored by many as being more natural than the MSSM, for example. In recent 1-2 years, the detailed analyses of the MSSM parameter space – various choices of the hierarchies between the superpartner masses (which particles may be lighter than others and why, and so on) was a vibrant field that developed dramatically and identified some previously overlooked possibilities.
