I don't think you're being nuanced enough. Wendy's in Montana is offering $17.50 an hour and not getting applicants. That's clearly a sign of some deep structural labor market issues.
Also $17.50 is an incomplete picture. How many hours per week? Any benefits? I would bet a years salary that it is <40 and no benefits. Would you take that job?
https://www.google.com/search?q=bozeman+montana+wendy%27s+hi...
Also, I don't understand why $13 is "obviously pathetic". I make a little over $15 an hour and I get by just fine.
/s
That sounds more like inflation than productivity actually going up.