But wouldn't it be more useful to have a course that emphasizes critical thinking about all types of problems rather than focusing on one specific application of critical thinking?
Teaching critical thinking early is a bad idea.
There is a place and time for shoveling as much information into a child's head as it can possibly hold without exploding. This is when we teach multiplication tables, drill grammar into their thick skulls, teach them basic math up through algebra, spelling, penmanship, history, and so on.
As soon as you teach critical thinking skills, it's like setting the write protect bit: it enables them to make a value judgement on the validity of the information they are being given by the teachers (and other adults), and as soon as you have that, you begin to build distrust of information sources - even ones with good information to impart.
Generally some critical thinking skills form on their own; creative writing, physics, chemistry, debate, and other classes tend to foster their development, regardless of whether or not you are done shoveling the basic stuff into their heads. As soon as that bit is set, you might as well give up trying to program them, you've lost: they're teenagers.
Logic classes belong in the first quarter/semester of your first year of college, and not before.