We have several family friends who do this regularly. What helps is there are no direct flights to their destinations. They leave with their US passport, and if they have to exit the terminal, go through customs with their US passport.

When it’s time to board, they use their other passport. At the destination, they go through customs with their local passport and don’t have to stand in long lines.

The only situation I’ve heard of is if they stay in the other country and make money while there, those may incur US taxes as foreign earnings.