The standard model does not explain its 20 parameters and does not contain gravity. The standard model is incomplete. Does the incompleteness of the standard model imply that experimental effects exist that contradict the standard model?
Not at all. The simplest scenario is that some yet unknown theory explains the standard model and its 20 parameters, that the explanation is valid up to an energy region close to the Planck scale, and that is all there is.
Is this scenario real? We do not know. Could the scenario be real? Yes, it could. This simplest scenario has been raised in discussions by various researchers. They always reject it. But all the arguments given by Strassler, Ellis, Arkani-Hamed, and all the other researchers boil down to wishes. They wish that the standard model is not correct. The arguments they give are all of the type "It is impossible that we already know everything."
Wrong, guys. It is well possible. We do have a theory that describes all of particle physics: the standard model. For reasons we do not know, it seems to be correct. Full stop.
It might well be that the search for effects beyond the standard model is similar to the search for the perpetuum mobile. The wish exists. But there is no way to realize it.