Well, I don't know if "making the theory fit the data" is always a bad thing I'm sure if you could explain electroweak symmetry breaking without a higgs, in a similarly economical fashion (i.e. not "extended walking technicolor"), then you'd be invited many places to give many talks. The situation with the higgs mass is a bit intricate---the ONLY way we know how to break symmetries is to give scalar particles VEVs. Naturally, scalar particles are heavy, but we have a spontaneously broken symmetry at a low scale. So what can we do? Similarly, you could ask why the electron should have such a small mass and the top quark such a large one. Or why all three neutrinos have more or less the same mass, but none of the quarks and leptons do.
PS Sverian---do you know a good review of the precision electroweak observables/data? I have this Phys Rept article by Heinemeyer, Hollik and Weiglein.