I think having both 14th and 15th Streets between K Street and Constitution Avenue primary is fine, as they are both equally-important routes, making it difficult to decide which one should be primary and the other secondary if both are not the same classification, my justifications for each being:

14th Street is the most direct route between US 1 and and 16th Street, making it most useful route for through traffic. It also links to The Mall.

15th Street is the first major through road heading east from 16th Street, and connects to the White House and monuments as well ass Maine Avenue and I-395 Southbound ramps, making it an important route for local traffic.

I would, however, keep 14th Street through Columbia Heights secondary and the street tertiary through 16th Street Heights. 14th Street is a quite important through CH, and through roads like 14th north of the area, which cross paths with many other major roads and/or lead to other major roads at both ends are typically good candidates for tertiary classification.