You also can't look at the market statically. Higher wages will create incentives for new people to enter the profession, increasing overall supply (and eventually putting some downward pressure on salaries once again).
That's true in theory, but I don't think there are a lot of people ignoring the tech sector because median pay for a competent engineer is only ~$100k.
Sure, you can find examples of people who went into other areas, but given the very low barriers to entry (put some good stuff on Github repeatably, no industry requirement for an advanced or even undergraduate degree if you have talent, no unions or guilds, no competency certifications required to practice software engineering), I don't think there's such a big pent-up supply.
I live in Australia and work in a small company and $100k just isn't enough to entice me to go over to the US to work for Google et al; It isn't that much more than what I make now, plus I get to live close to home. And yes, I can choose to move to US if I want, due to the E-3 visa.
There are a lot of people like you even in the US. Cost of living in California is part of the issue. Tech companies could find the talent for less pay if their workforce was located outside the most expensive areas.
Wall Street pays much more. Anyone looking for the most lucrative sector to cash in mathematical talent would pick finance if choosing purely based on salary.
100k is a lower salary (adjusted for inflation) than high school dropouts were making in the dot-com boom doing things like server administration for companies like Go/Disney.
That's not the point, though you're right. The point is that $100k is still a lot of money when the median is ?$47k. What are all these people doing instead of accepting a measly $100k to be software engineers? I don't think 4100k jobs are so easily available in the US that people are just turning up their noses at it, but that there may be other reasons (like lack of appropriate skills) for the lack of supply. Of course more people will try to enter the profession if salaries are allowed to rise to a market equilibrium, but SW engineering skills aren't a simple commodity that people will just automatically acquire in accordance with the laws of perfect competition.
TheCoelacanth is looking at the market over the short and medium term, which is the correct way to look at it if we're arguing over whether there is a shortage today.
Furthermore, it's not like quantity supplied is perfectly responsive to price. It takes time for new people to enter the industry.
Talking about the long-term is rather pointless because technically, from a theoretical standpoint, everything is supposed to equilibriate over the long term. All shortages self-correct over the long term. Again, this is theoretical.