Producing software, in, say, Romania, and selling it in the US is a perfectly viable business model.

In which case the software shop is in Romania, not the US. Not sure your point.

If your goal is to employ more people in the US software industry, you've kind of shot yourself in the foot.

There are also good reasons to want to employ people who are 'closer to the client'. Plenty of places have engineers both in the US and elsewhere. Lots of companies just want to employ the best talent from wherever.

Make those things difficult though, and software is about the easiest industry to route the work abroad.

By "difficult" I assume you mean for higher pay as supply and demand dictates.

And as for the supply, everyone talks about US grads not going into STEM as if it's a law of nature. If salaries were allowed to keep going up during these temporary hot markets, more of the best and brightest would be attracted away from medicine/law (the current default choices for top students). STEM has always been a stepping-stone for the lower-middle class, not a particularly prestigious profession in my lifetime (at least compared to what someone of the same intelligence could have otherwise done). Now it is being turned into a stepping stone for the middle class from developing countries, again driving those domestic students away. (I work in education and see this every day).

Why would salaries go up that much when you can just hire people directly in Romania or wherever?

I think you are failing to grasp that this is a global market for talent. Sure, being local helps some, but if the disparity is too great, companies will move. Also, there is not a fixed lump of labor to go around.

I can grasp the concepts just fine. Being local helps immensely. The disparities are correspondingly immense. More so when you consider the high unemployment rates in developing countries.

Also there needs to be sufficient talent available across all roles needed, to completely move the company to a new location. As opposed to just a lot at the low end of skills. The cost and other downsides of that move would also be immense.

Perhaps one day remote work will be far more common, and I think this would be a good thing, by the way. I also think brain drain is bad overall. Developing countries need those productive residents far more than the west does.