No opinion on math PhD but I’d still strongly recommend math major.
Most of us never reason. A situation arises, we act intuitively, then get RL’ed. At best we get anxious and bounce between limited hazy alternatives.
But to prove a theorem you have to reason. You don’t know what precision or thinking really is until you have to sit and struggle to prove a theorem that’s new to you.
The crazier the world gets, the more this skill is useful. And the world is about to get very very crazy.