I realize that there have only been four in major league history. Most recent was in 1989 although he only played a few games for the Pittsburgh Pirates. Even as a two-way player, it will only what you pitch right hand when you’re a catcher as your secondary position.
Also, why can’t we select multiple positions as our secondary position? Look at how many multiple position players are in the game now. It’s never been uncommon for a second baseman to also play shortstop. But there are so many players in the major leagues right now they can play almost all positions.