You are correct, "cull" the heard. By age 14 the boys have gone through their first growth spurt and their skill set is fairly well developed. The physical size difference between the 14 and 15 year olds isn't that great. Top talent at 14 can compete against 15 year olds without difficulty. The DA is purely about top talent.
With regard to this comment: "I don't understand why US soccer would keep adding clubs (and some mediocre ones at that, but that's a different topic) and ages and not spend that same money instead to keep a single age year."
Taking a step back, the USSDA pays nothing to DA affiliated clubs, it just manages the Development Academy league/program. The DA has adopted a pyramid structure that intentionally "culls" the heard as they reach U18. Because the National Team does not exclusively select from the USSDA, the USSDA doesn't care if some kids are lost and move to other programs (ODP, NPL, go to Europe, etc.).
Its costs the USSDA nothing to add lower level age groups because those costs are solely borne by the Clubs. The USSDA's model is to say to both tiers of clubs (MLS and Independents), you guys must solely bear all costs to participate in the DA program and you get nothing if your investments in these kids pays off ... unless you are an MLS affiliated DA program, in which case you get a "Homegrown Player" exemption that has value. For the non-MLS affiliated clubs, the DA is purely a marketing play that keeps their clubs competitive with the market and they support the DA teams through increased club fees to the non-DA teams (all those SCDSL, CSL, etc., teams).
The USSDA is also pushing hard for DA clubs that have U15/16 and U17/18 to have residential academies. If the USSDA were to add a single age group for U15, it would increase costs by a factor of 33% because we would have 3 teams instead of 2 teams. The MLS affiliated teams don't really care that much, but the Independents do.
So yes, culling is built in to the pyramid structure of many U12 teams and few U18 teams.