About seven years ago we implemented "full zoom" in Firefox 3. An old blog post gives some technical background to the architectural changes enabling that feature. When we first implemented it, I expected non-integer scale factors would never work as well as scaling by integer multiples. Apple apparently thinks the same, since (I have been told) on Mac and iOS, application rendering is always to a buffer whose size is an integer multiple of the "logical window size". GNOME developers apparently also agree since their org.gnome.desktop.interface scaling-factor setting only accepts integers. Note that here I'm conflating user-initiated "full zoom" with application-initiated "high-DPI rendering"; technically, they're the same problem.
Several years of experience shows I was wrong, at least for the Web. Non-integer scale factors work just as well as integer scale factors. For implementation reasons we restrict scale factors to 60/N for positive integers N, but in practice this gives you a good range of useful values. There are some subtleties to implementing scaling well, some of which are Web/CSS specific.
For example, normally we snap absolute scaled logical coordinates to screen pixels at rendering time, to ensure rounding error does not accumulate; if the distance between two logical points is N logical units, then the distance between the rendered points stays within one screen pixel of the ideal distance S*N (where S is the scale factor). The downside is that a visual distance of N logical units may be rendered in some places as ceil(S*N) screen pixels and elsewhere as floor(S*N) pixels. Such inconsistency usually doesn't matter much but for CSS borders (and usually not other CSS drawing!), such inconsistent widths are jarring. So for CSS borders (and only CSS borders!) we round each border width to screen pixels at layout time, ensuring borders with the same logical width always get the same screen pixel width.
I'm willing to declare victory in this area. Bug reports about unsatisfactory scaling of Web page layouts are very rare and aren't specific to non-integral scale factors. Image scaling remains hard; the performance vs quality tradeoffs are difficult --- but integral scale factors are no easier to handle than non-integral.
It may be that non-Web contexts are somehow more inimical to non-integral scaling, though I can't think why that would be.