Web browsers are not that kind of software. The web is evolving much faster than any of the other things you mentioned. New features get proposed every year, and you just have to deal with it and implement them, even if they complicate the implementation of the browser. Even if you cut that off, you still have to deal with the horrific mess that is the cumulative total of past web-related decisions.
There's certainly a layer of a rendering engine—the part that translates a CSSOM into rendering pragmas—that changes a lot over time. But rendering the resulting pragmas itself doesn't change much, and features requiring new pragmas come about remarkably slowly.
Clearly, though, you know what a rendering engine is, so I'm not sure what your argument in the GP post was. Was it just a tangential statement (i.e. "rendering engines are well and good, but it'd be silly to write the browser itself in Rust, for [reasons]"), rather than a rebuttal...?
In the case of startups, their goal is to sell out way before the maintenance phase of the lifecycle. So, it doesn't really matter to them so much as quickly getting out working features. In other cases, esp long-lasting endeavors, then this is a good point to consider.
Or grow so quickly that replacing most the legacy code from a year or two ago is not a significant hurdle at their new size.
In this vein, I wonder if there's actually a third path that might be better than both. Using a low-level but fairly expressive and strongly typed language but very loosely, such that it allows you to iterate fact but with less performance, and you can come back later and replace chunks as needed, but with the same language. I don't have any real experience with that, and I could see it going either way for a number of reasons, but it seems like we have more languages that might fit that criteria now (or at least they are more popular now) than we have previously.
Some projects are written as explorational prototypes or MVPs. I don't think anyone is saying Rust is much good for those.
But (numerous) other projects are written as "the first real Quality implementation of [well-known problem], using a decade's experience with other implementations." Much of the common software we use—{server daemons (HTTP, SSH, DNS...), parsers and encoding libraries (for XML or JSON; JPEG or PNG; MP4 or MKV...), databases, load-balancers, distributed queues, ...}—fits this paradigm.
If you're writing Nginx, or Redis, or djbdns, you aren't "adding features" out of some agile user-story kanban; you're carefully implementing a small, curated set of well-known, well-understood features, with much research done to ensure that you arrive at the best and least fraught implementation, the one that will make people prefer your software for its quality and reliability and set-and-forget nature.
Rust is for that kind of software. (Which makes sense, given that Mozilla's Servo rendering engine also has the goal of being that kind of software.)