To flip it around, I think what you're saying could be used to present an argument that it's silly to be talking about a lack of qualified STEM workers in the first place. I'd agree that STEM degrees, and therefor workers with STEM degrees, are not interchangeable, so we therefore should not be grouping them all together as 'something we need more of'.
Why are we all using this 'STEM' acronym now anyway? All of the sudden we're all using a new acronym that doesn't serve to make the discussion any more clear, which to me is a clear indication that the discussion is being manipulated by someone. So what are we really talking about here? When we're talking about the need for more 'STEM workers', we're just talking about engineers, right? Most likely software engineers, I'm guessing, since I only hear about it in reference to Facebook and Microsoft complaining that it's too hard to hire programmers.
I'll tell you, there are plenty of programmers out there. There's not a shortage. You might respond by claiming that most of those programmers aren't too brilliant, but the truth is, there's always a shortage of brilliant people in any field. So what, exactly, are we talking about here? As far as I can understand, we're talking about software developers complaining that there's a shortage of a glut of programmers that would allow them to treat programmers as minimum-wage interchangeable cogs in a machine.
So you're right, 'STEM' is too broad a term and is insufficient to describe the issues we're facing, so let's just not use that term. It's a term that was most likely invented to obscure what the discussion is actually about, so let's try to be more descriptive.