Oh, no, it’s not that I don’t believe you. Just sounds like there’s different opinions within the military on the usefulness of burst fire.
The M1a Springfield uses a totally different manual of arms than the M4/M16, especially when you fix the magazine.
If we’re trying to square the 2nd amendment with reducing mass shootings (a very small but spectacular number of gun deaths) everything you listed would improve the situation slightly and there’s little reason why we shouldn’t have them. I’d throw in a storage requirement requiring guns and ammo be kept behind a lock. But mass shootings are much more of a social phenomenon than anything else. We’ve had access to capable guns for a very long time and mass shootings only became a thing in the 90s. That is, it’s not inherit to humanity, it’s cultural. (This should be further evidenced by the fact that they’re all done by white guys.)
Now, that sounds like a cop-out, but it’s not. It’s saying that we know we can have a society with guns and without mass shootings because we used to have exactly that. Well, what did we have then that we don’t have now? Lower inequality, higher union representation, more accessible housing, less media saturation, higher minimum wage, fewer monopolies, etc. I would suggest reading Angry White Men by Michael Kimmel to get an idea of the kind of person and situation that produces mass shootings. There’s a racial component to it that won’t (and shouldn’t) change, but so much about our economic and social situation can change to get rid of mass shootings. Heck, even just Medicare for All would have a big impact, since it would make counseling free and accessible. Plus, all these social changes would have an even bigger impact in the other major areas of gun deaths, murders and suicides.