The running of the coupling constants is necessary because this is what you observe when you look at EM, weak force and strong force interactions at high energies. The fact that it flows naturally from the procedures you to renormalize and hence to make it possible to do calculations is just an added bonus.
The strongest evidence to date that there are no more particles in the Standard Model are:
(1) W and Z boson decay are "democratic" which is to say that they produce all mass-energy conservation permitted particles in equal amounts (subject to some well understood tweaks). So, weakly interacting particles lighter than the W or Z boson are forbidden. Also, if there was a weakly interacting particle with mass lighter than half the Higgs boson mass and more than half the Z boson mass, the Higgs decays would also be much different than those observed.
(2) Particle-antiparticle creation from high energy photons provides similar assurance with regard to charged particles.
(3) We are able to fit all of the collider data with the particle set of the Standard Model (of course, fitting astronomy observations such as dark matter and inflation and gravity is another matter entirely).
(4) The experimentally observed unitarity of the CKM matrix leaves very little room for additional particles along the lines of SM4.
(5) With a Higgs boson of the mass observed, the equations of the SM don't break down anywhere up to GUT scale energies (as the would at some other Higgs boson masses). So, we don't need a new particle, for example, to keep the probabilities unitary up to an arbitrarily high level.
The SM exclusion of right handed neutrinos and other particles is simply Occam's Razor at work. The SM doesn't need them to explain what is seen so a minimal particle set and force set is assumed until we learn otherwise. For several decades, we needed to Higgs boson for the SM to work even though we didn't see it, so it was inferred. But, no data requires more than three generations of fermions, and no data requires more than the known bosons to explain anything but gravity/astronomy.
