Seems to be some confusion between the Half-Tracks. The M5 and M17 Half-Track was an export model for the Soviet Union and other countries, the United States used the M3 and M16 Half-track as well as others based on the M3. That said, it makes no sense that Relic added the M5 Half-Track to USF, since we never used that version in war, it's like giving USF a T-34/76 because the Soviets gave us two of them in 1941.
I'm assuming the real reason USF got an M5 was because Relic couldn't be bothered to model the M45 on the newer M3 model. Not like it matters much anyway because the M5 model doesn't look like an M5 anyway, and is in-fact just the M3 model from CoH1, renamed.
I understand the historical fact that M5s were mostly lend-leased, with M17s mostly to the USSR.
I also agree with your assumption that Relic most likely didn't model an M16 Multiple Gun Motor Carriage in CoH2 because they had an (almost) look-alike in the form of the M5/M17.
I disagreed on the poll since the issue was minor--cosmetics are cosmetics, after all. If relic put the M3 in the doctrine and coded it to allow an upgrade into an M16, it that would be fine with me, no need to make a brand-new 3D model or put new skins on it.