Not sure why NA is being singled out here. Bottles are largely the same shape (with a few functional differences, see below) no matter where they come from.

The round shape is mostly a historical artifact from early designs that were hand-blown. A hexagonal (bestagons!) shape would pack better in an infinitely large container, but since most shipping crates are rectangular, there will be wasted space either way, and round is far easier and cheaper to mass-produce. Also, as a carbonated beverage, sharper corners could create stress points and exploding bottles.

Toppling over could potentially be reduced with a wider base, but fitting in the hand is a hugely important factor for any drinking container. There are larger-based bottles, but they also need more specialized packaging and storage space. By using bottles that are similar size to aluminum cans, lots of infrastructure can be dual-purpose (I'm thinking of things like can/bottle storage in your refrigerator, for example).

Double the volume of what? Glass bottles have to be thicker than other materials, so to get the same volume as a can with the same size base, it has to be taller.

If you want to do a lot more reading, here's a few sources I borrowed from:

https://sha.org/bottle/beer.htm

Regarding the functional design features referenced above:

https://www.hillebrandgori.com/media/publication/beer-bottle-sizes-and-their-surprising-history

Those ‘shoulders’ we keep mentioning remain in modern beer bottle design mainly for aesthetic reasons. Their original function was to provide a handy place for the yeast residue and dregs to collect, so that these didn’t pour out into the glass with the beer. Nowadays, most beer is filtered, so this design feature is no longer needed. Unless you’re bottling a yeast beer like a Belgian beer, of course.

Sounds like it’s time for a stubby.

NA = North American or non-alcoholic?

From a European, what does a standard NA beer bottle look like? I thought your bottles were similar to ours, which means bottom heavy and a slim neck.

Have they? Can you give an example? Any NA beer I've bought (which is quite a bit) has been in standard beer bottles. Assuming you mean non-alcoholic, right?

I've never really seen an issue with the standard glass beer bottle in North America, is there a superior bottle shape that I've been missing all my life?

More and more craft breweries are going can-only. It's better for the beer and the environment.

I only drink my beer by the growler.

The "stubby" bottles were replaced with tall "classier" bottles in a surge of .. fashion-moment, or something.

I remember somebody did a news vid, or documentary on it, & the industry lost usable-storage-effectiveness when they went with the taller bottles, and there's more glass in them, too..

They said if they'd known what the actual results would be ( it didn't alter the market to increase the percentage of the population which is always buying beer, for some reason.. ), they wouldn't have done it.

Well, Duh..

"never believe your own hype" IS a rule, because when you're believing your own marketing-bumf, then you're not competent at calculating any sort of project balance-sheet, right?