This is a case of seeing the problem and misdiagnosing the cause, I think. Though I give it credit for original thinking and I at least appreciate it from that angle.
The basic thrust seems to be that algebra isn't necessary because most people, including a lot of people you wouldn't think didn't need it, don't use it in day to day work. And it hasn't improved the overall citizenry -- meaning they don't take it and apply the thinking to daily life. And that is true. Both parts. I jump to a different conclusion though: most people learn enough to pass the tests but don't internalize it to the point where it becomes part of their critical reasoning. They don't abstract algebra from algebra and go on to logic. They don't use the more direct algebra to avoid doing brute force arithmetic. They don't use algebra to fact check reasoning they hear.
So my counter is: We aren't teaching it. We're just going through the motions. And yes, you can't justify the results of going through the motions, because the results stink.
We need to teach it. More comprehensively. Not abandon it.