Earlier quoted context omitted.
Correct the web version is not a 1:1 swap but the desktop version has been a stable product used by millions for decades. Most users use the desktop version and indeed it has few compatibility issues with itself.
Well the point wasn't "desktop vs. web version" but showing that compatibility issues are common even within the proprietary products of a single vendor, something which one of the previous comments implied wouldn't be the case. If you have to fixate on a single, non portable product (lets not talk about office for Mac) then you can easily get consistency from LibreOffice as well.
Different file formats. Different software entirely. Compatibility issues would be orders of magnitude more impactful than any issues intrinsic to the O365 suite.