There is a process unfolding here, and it may seem harmless, but it ain't! First the progressive theorists come along and hollow out "classical" music as being somehow sexist, racist or imperialist, then they define away more and more of its essential characteristics. In the name of diversity or popularity "crossover" artists and repertoire are included and finally, coverage of classical music in the mainstream media is more and more eliminated.
What do we call this? It is a process that has emptied out a lot of other traditional institutions. It is emphatically not "popularizing classical music" as that would involve, above all, public education. No, what we are seeing is rather the devaluation of classical music qua classical, the vampirical draining away of the life-blood of the art form. Let's create a new tag for this: "eradicating classical music". There are lots of clever ways to do this and making it simply disappear from public awareness is one of the best.
Nothing against Sting, of course. I am rather a fan of him as an artist. I enjoyed his foray into Dowland and his accompanying of a dancer with the Prelude to the Cello Suite No. 1 by Bach on classical guitar. He is an all-round musician. But I wonder at his accepting this prize. He surely doesn't need the money and wouldn't it be a very good point to make if he said "thanks for the honor, but I am not primarily known as a classical musician, so why don't you give it to someone who is?"
Of course, the basic problem of classical music is that it is, without a doubt, elitist in the sense that it mostly appeals to people with a lot of education in the arts and with honed sensitivities. Historically, these people largely belonged to the aristocracy and had the resources to support the art form. Nowadays, it is opened up, democratically, so that everyone who wishes can enjoy it. But it is an art form that cannot be completely successfully commercialized without turning it into something else. It still needs that support from a small minority with taste and funds. Alas, we have the 0.001% of frightfully wealthy people, but they tend to spend their money on other things (though I read that Taylor Swift made a large donation to a symphony orchestra a while back).
I think that classical music will survive if only due to its inherent quality--something that is rarely captured in definitions of what "classical music" is. But trying to popularize it by turning it into something else, or by making it the instrument of social or political movements, is not the right strategy. The only good strategy I know of is to simply create and perform music in the best way we can, win a few audiences, and introduce as many people as possible to the music. Nothing wrong with that.
Let's listen to a youth orchestra to hear how this works. This is the Simón Bolivar Youth Orchestra conducted by Gustavo Dudamel playing the Symphony No. 3 by Beethoven in a concert in Bonn in 2007: