As far as I know, Firth hasn't done a lot of theater work. When he was young he was in the play Another Country and was then cast in the film version.
It is so arduous to do a musical, especially a lead. I do agree with you that it would be even better to see him in a play. He certainly doesn't need the work, his film career is still strong.
Maybe this is a tryout for a film version which has been talked about for years. Emma Thompson wrote a screenplay and had wanted Firth and Carey Mulligan to star. Though Mulligan wouldn't be able to handle the score.