To add to this:
1) The M14 (and M1A by extension) had a HORRIBLE initial rollout. Springfield Armory designed the M14 as a M1 derivative, created a pilot run, earned buy-in on expanding production, and then the MIC bungled the follow-up. Winchester and Remington were comically low bidders who delivered terrible quality control for the first few years, leading to SA to continue receiving orders despite the intention for SA to stop production after the pilot run.
This lead to a belief that the M14 was a bad rifle due to QC issues, despite a sound design. This belief lingered on while the USAF ordered small numbers of M16s to supply base guards. These didnt have the horrific QC issues that Winchester and Remington M14 experienced, leading to other branches ordering M-16s under the rationale that "at least these rifles work". The upswing in demand for M16s exceeded M14 demand until production of M14s eventually ceased.
2) 7.62 has AP and barrier penetration advantages over 5.56 NATO. You know what the US DOD was shooting at during the period of M14 production? North Vietnamese guys in flip flops hiding behind foilage. 5.56 goes right through that without difficulty.
3) I second your point about ammo weight. 7.62 is heavier, larger (i.e. you can carry fewer rounds), and more costly. The primary purpose of small arms is suppression so you can kill the Opfor with artillery or crew-served MGs, not Private Snuffy's "Big honkin battle rifle".
4) I second your point about rifle and kit weight. If you've never tried to run with a M1, M14, or M1A...you should. You will learn why a few pounds matter.
5) Followup shots are faster and more accurate with 5.56 than 7.62. Both due to the inherently higher recoil of 7.62, and also because the buffer spring on the M16 SIGNIFICANTLY reduces felt recoil. And this isnt a "hur dur get stronker". It's physics.
To further add the AR15 is a highly modular platform with an excessively large aftermarket for any kind of part you may want. You have the option of building multiple uppers in differing chamberings, barrel length and accessories that can be swapped onto the lower in seconds.
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