Obviously there is no way to really predict when this would happen, but I don't think it will be up to developers to decide whether it happens or not. In Texas for example, the legislature forced engineering to be professionalized (or regulated) in an emergency session after a school in a well off area exploded in a gas explosion (https://en.wikipedia.org/wiki/New_London_School_explosion#In...).
I also do not think this is limited to software engineering. Medical doctors and accountants have faced the squeeze in recent years too. There are tons of (bad) DO med schools opening up across the country that will be flooding the field before long, nurse practitioners and physicians assistants get to do more and more work that only doctors got to do, and more and more accounting is being offshored. The question is when things get so bad that even the powerful decide to actually do something about it.
I also do not think this is limited to software engineering. Medical doctors and accountants have faced the squeeze in recent years too. There are tons of (bad) DO med schools opening up across the country that will be flooding the field before long, nurse practitioners and physicians assistants get to do more and more work that only doctors got to do, and more and more accounting is being offshored. The question is when things get so bad that even the powerful decide to actually do something about it.