If "thinking mathematically" is the actual, vital part of that education, for most students, I have some doubts that a classics-based approach is any worse than the modern kind. Maybe better, except for a small slice of students who will continue to engage with advanced mathematics after they finish undergrad and do need the modern version.
So maybe it's not a bad thing that people graduate from College are required to take a few algebra and stats classes when they're ostensibly running the show at large corporations and in various levels of Government.
Kinda had to gently remind them that the physics they knew wouldn’t help them with ontological problems like “what is an object?” but once they got over that hurdle everything was pretty much fine.
Word problems are the last edifice of natural philosophy in the high school mathematics curriculum and there’s constant pressure to remove those as well.