As far as I can tell, the central premise of their article — that the child credit is the reason the Lee-Rubio tax proposal doesn’t bring the top tax rate down to the low 20s — is false. If the senators got rid of the expanded child credit, they would have enough extra revenue to lower all tax rates by about three points (judging by this chart from the same source on which Shlaes and Denhart rely). That would mean that instead of cutting the top tax rate from 40 to 35, they would cut it from 40 to 32. You would get improved incentives and perhaps stronger growth as a result, but it would not be much; and at the same time you’d lose a lot of the political attractiveness of the proposal. (You’d lose a lot of the substantive attractiveness too, but I don’t expect them to agree with that.)
You could bring the top rate down lower than that if you left the lower tax brackets alone, but that’s a political non-starter for reasons that have nothing to do with the child credit.