There's a huge and important distinction between “we should try to teach all kids to code” and “all kids should be able to code”, and it tends to get lost in the discussion.
Programming just isn't for everyone (and that's OK), but everyone should give it a try to find out.
Agreed - we teach math in schools not to make everyone top talented Mathematicians, but to teach a skill that might be useful in life.
Teaching programming in schools would probably get the same result was teaching math: courses that normal people promptly forget a year after school. Because, really, how often have you factored a polynomial?
But still, you got a little taste of Math in school. Maybe you liked it, maybe you barely made it through math. Same thing would happen with mandatory programing classes.
Thinking the talent crunch will be solved by teaching CS as part of mandatory education is probably wishful thinking.
Programming just isn't for everyone (and that's OK), but everyone should give it a try to find out.