Measurements of the Higgs boson quantum numbers, on the other hand, provide very useful expansions of our understanding. The parameter space of possible Higgs bosons is so large that its impossible to know where it could be and different regions correspond two very different possible physics. So the measurement of the Higgs' mass, spin, couplings, and even the number of Higgs bosons are actually quantitative improvements to our understanding.
The problem is that if you're not a physicist, it is very difficult to explain to you why this measurement is something more than empirical. Lay people can easily understand that a new particle has been observed, but not so much how that expands our understanding.
I'd also like to point out that most of the people who came up with the ideas that are being tested are still alive. The standard model as we know it didn't really start taking shape until the 1970s.