People (including me) often say that barriers to entry are low, but I think it's a bit more complicated than that. There are no legal barriers to entry. But barriers to being a "mathematician" are also low. But would you say that the barriers to doing meaningful mathematical work are low? It's out of reach of most of the population.

Anyone can hang out a shingle as a software developer, but are the barriers to getting through the technical grilling typical of a software interview process really low? Just because there are no legal barriers doesn't mean that it's an easy thing to learn.

I don't think that software engineers are suffering from bad pay, but is the pay high enough that it makes sense to be talking about a severe shortage that the government should start fixing? Based on pay, I'd say we should take the "software developer" shortage about as seriously as we take the "dental hygenist" shortage.