That sounds backwards to me. Using standard fonts is how you achieve consistency. Using a custom font for just your webpage is not helping me (the user) get consistency at all. That's what 'standard' means.
(Frequently, custom fonts also hurt readability, which is why I hit "reader mode" on nearly every webpage these days. Every single day I run across webpages with custom fonts that I literally struggle to read.)
The situation is just like early versions of Mozilla or Java, where they used the same UI toolkit on all platforms for "consistency". Eventually, programmers realized that users tend to switch between applications more often than they switch operating systems, so the way to achieve consistency for actual users is to match the local environment.
> Variability in system fonts means [...]
Yes, all of those are real problems. That's why I've set up my web browser in a way that results in legible text for me. As per the Pottery Barn Rule, if you use a custom font, you're taking responsibility for all of these issues -- and you're going to screw up at least some of them (or something you didn't think of), and I'll hate your webpage for it.
