Many cellists have adopted Schnittke's Suite in Old Style as their own, although it was originally composed for violin and piano (or harpsichord). I would argue that it sounds better with harpsichord. Since this work has made it into the violin canon, it's really easy to think that Schnittke was somehow innovative in using a harpsichord in 1972. After all, he continued using the harpsichord in his later works like the Concerto Grossos and the Hymns. But the harpsichord was in the air of Soviet music and Schinttke was just catching a well-established wave.
Growing up in the final seven years of the Soviet Ukraine, the "golden age" of Soviet cartoons was a part of my steady diet. And why not? These cartoons had great stories, beautiful illustration, and amazing music, written by the best composers of the Soviet era. I didn't grow up in a musical household. Unlike my kids, who can recognize Bach, Beethoven, Tcherepnin, and Jemnitz from the first four notes, names like Shostakovich, Weinberg, Gladkov, and Boris Tchaikovsky were meaningless to me.
Why am I talking about cartoons? Because four mega-hit cartoons that used harpsichord preceded Schinttke's Suite all in the 1969-1972 timeframe. Three of the cartoons were about Winnie the Pooh, with a brilliant score by Mieczysław Weinberg; and a cartoon about the Bremen Town Musicians, a 25-minute musical by Gennady Gladkov (who is still living, by the way). The use of the harpsichord was very much neo-baroque in these cartoons, like in Schnittke's Suite. Another prominent piece which used a harpsichord was Boris Tchaikovsky's Partita (1966) for cello and chamber ensemble (composed for Rostropovich).
I would highly recommend that my readers listen to these cartoon soundtracks and the Tchaikovsky Partita. All of them are available on YouTube.