Gilbert reckoned that "The Gondoliers" would last throughout the twentieth century, and in "The Pirates of Penzance", the plot device expires in 1940. (And Japan copped it in 1945.) But a modern young audience has any amount of new silly songs to choose from.
CBeebies (BBC for toddlers) is putting on "The Tempest" today. From looking in, they cut away frequently to William Shakespeare explaining the action to one of his Kickstarters, they get through it in about an hour, and I'm nearly sure that Sir John Gielgud in the buff won't be involved. If you'd prefer to see the Clangers, I don't disagree. :-)