> If it was to match inflation it would be more than $15

Neither of your sources support that claim:

> Even worse is that federal-minimum-wage-earning workers today are paid 31% less than the $10.54 an hour they would have been paid in 1968, when the minimum wage reached its highest (inflation-adjusted) value. [1]

> The wage hit its peak in inflation-adjusted terms in 1968 at just over $12 [2]

The productivity argument is silly, and your third source says as much. Minimum wage has not kept pace with average productivity because minimum wage jobs themselves have not kept up with average productivity. CEPR makes the argument that doctors and software engineers just make too much money, and this somehow hurts the minimum wage earners. Which is a wild bit of mental gymnastics to claim that minimum wage earners should profit from high-skilled productivity, but the high-skilled workers should not.

Tying minimum wage to productivity never made sense to me. Obviously as technology progresses, productivity would increase. There wouldn't be an incentive to invest in productivity-increasing tech if it was directly offset by wage increases.

Tying it to inflation though is a no-brainer. We do it for social security payments, congress salaries, etc. There's no justifiable reason for not doing this.