In researching this (which I should have done before shooting from the hip) I found out quite a lot. Aviation lighting is currently controlled through two source documents SAE 8017A and SAE 8037. In reference to this two documents the FAA wrote FAR 23.1387-FAR 23.1397. All aircraft lighting has to conform to these standards. I believe these LED bulbs fail on two fronts. First, they do not conform, or do not have a C of C for conformance to any current standard. The Mil-spec they give is no longer current. All through the SAE documents the standard for aviation red, green, and clear lights are specified.
Secondly, The light systems in your aircraft were approved to a TSO. To install these lamps in those systems degrades the system and takes them out of their TSO approval specs. It changes the specs on light output, amp draw, chromaticity values, and heat dissipation. So if you put these lamps in your Whelen or Grimes parts, they become unairworthy for failing to meet the TSO. Chromaticity is the color and intensity value. Tests must be done to ensure no bleed over into any other light spectrum so as to not cause confusion to pilots on what aspect they have on an approaching aircraft.
I concluded that these LED bulbs fail to meet any current spec. And if they did they would need their own mounting system and a TSO to be used on a certified aircraft.
All the above is just how I read it. Your viewpoint may be different.