When Merman and Martin were at their peaks, cast albums were among the top selling records in the nation. That's how someone like Mary Martin could become a household name, even before she appeared on TV as Peter Pan. (Once she did that, of course, she was forever a national celebrity.)
But even Merman, Martin, Julie Andrews, and Barbara Cook (to name a few) made regular visits to TV on variety shows, specials, and spectaculars.
The world has changed too much. Now, the biggest star names for the stage are people like Hugh Jackman who achieved their greatest fame elsewhere and can use it to bring people to their first love.