I'm not sure why the attestation of airport approval for Cats C and D, but then that part of the process all occurs well before I get involved.
You'll see a LOT of airports out there with shortish runways that have Cats C and D on the chart. That's because unless advised otherwise, I might as well design for Cat D. If the design works, why not?
From a procedure design standpoint, in the vast majority of cases, there are only a few things that are affected by the higher Categories, and it's pretty much just anything involving a turn - meaning a turning missed approach, leg length of a segment that begins or ends with a turn, Procedure Turn length (but only if you need less than a 10 nm length, which is rare), Circling minimums, and such. Because faster airplanes take longer to turn. There are glidepath angle limits too, but with most procedures at 3.00 degrees, that meets everything.
For a straightforward, generic, straight-in RNAV approach with a straight-out missed approach, none of these factors are likely to come into play. Okay, it's a 3000 ft runway. But hey, there's no reason to restrict Cat C or D, so why not publish it?
Cat C and D used to require a larger area to be evaluated for the "visual segment" of the approach (that portion below MDA or DA). This did cause some problems for the faster airplanes sometimes, but that larger area was done away with several years ago.
The main effect we're seeing in recent years is with Cat C and D circling MDAs. When the radii for the evaluated areas changed some years ago, this caused Cats B, C and D Circling MDAs to generally increase across the board. Especially for Cat D, sometimes this resulted in a dramatic increase, so Circling restrictions (like "Circling NA for Cat D N of RWY 9-27") may have been implemented. Or, in some cases, "Circling Cat D NA" entirely. But since there probably aren't a whole lot of Cat D aircraft doing circling maneuvers anyway, this effect is largely academic.