As I see it, before the Higgs was seen, this search was also a search for "new physics", because if Higgs was wrong, a lot of new physics would have been needed

As I see it, before the Higgs was seen, this search was also a search for "new physics", because if Higgs was wrong, a lot of new physics would have been needed to explain the things Higgs was trying to explain. It's just that everybody was expecting a confirmation because all of the rest of the SM turned out to be right so far, so nobody really expected new physics to come from there. Now since the last chance of "new physics" due to the lack of a signal where a signal should have been is gone, everybody turns their hope to finding a signal where no signal was expected. This is of course totally legitimated, but it doesn't take away any of the importance of the former. I would love to see something new too, but if the SM explains everything we are able to measure today just fine, then be it. Then the SM is all we need, until we are able to measure more. It's just like the people in the 19th century: they had to go with Newton because they couldn't measure anything beyond Newton. But on the other hand, back then Newton was all they needed, because Newton could explain everything they saw.