My Thinking-
Higher sample rates result in better digital summing because every extra "snapshot" will result in more detail and "math" and reduced decimation.
Don't feel bad, this used to be my thinking as well, based on what I'd learned about A/D converters in electronics school back in the early 70's.
Back then, what we saw were 8-bit R-2R ladders, used primarily for data acquisition and telephony multiplexers. Audio recording in digital was an exotic new thing back then, something you did with ultra-expensive custom-built gear. Things have changed a lot since then, as I discovered when I later revisited the topic in an attempt to understand converters better.
I won't attempt to explain why your logic is incorrect because I'm just not that good at explaining stuff, and frankly some of the math is over my head.
I can, however, recommend one source that did a pretty good job of explaining the Nyquist magic theorem -- a book by Nika Aldrich called
"Digital Audio Explained for the Audio Engineer". Parts of it are mathematically intimidating, but he does a good job of illustrating how the audio is reconstructed from as few as two samples per cycle -- something that is not intuitive at all!
Until you have a chance to read the book, here's the bottom line, which you'll have to take on faith for now:
Nyquist says that you can encode and subsequently recreate ANY waveform EXACTLY as long as you sample it slightly over twice the highest frequency you need to record. This is hard to comprehend at first, because it's non-intuitive. The operative word here is
EXACTLY -- not a reasonable approximation, but an
exact image of the original waveform. No kidding. And with as few as two samples per cycle.