Even if there are some more cases, the basic point is still true: The majority of additions don't warrant word-size wrapping and it has been a source of many, many bugs.
> Addition modulo N is used only in niche cases ...
and not modulo 2^N.
The point that I would make is that general purpose CPU's doing general everday tasks such as https connections, secure transfers, GIS mapping, etc are doing a great many more modulo operations than acknowledged above.
... and niche cases like GIS location computations on a spherical planet and any form of engineering | physics mesh computation.
It's inescapable when you peer into the guts of any earth based modelling from satellte data .. something that happens on a daily terrabyte scale.