On many systems (e.g. OpenBSD) they're implemented with the exact same code. glibc is something of an outlier given its insanely complex implementations interacting with RedHat's backward compatibility promises. Many of the code paths are the same[1], but getaddrinfo permits stuff like parallel A and AAAA lookups, and minor tweaks in behavior (e.g. timing, record ordering) often break somebody's [broken] application, so I'm not surprised some people have stuck to gethostbyname, which effectively disables or short-circuits alot of the optimization and feature code.

But, yeah, browsers in particular do all sorts of crazy things, even before DoH, that were problematic.

[1] As a temporary hack to quickly address a glibc getaddrinfo CVE without having to upgrade (on tens of thousands of deployed systems) the ancient version of glibc in the firmware, I [shamefully] wrote a simple getaddrinfo stub that used glibc's gethostbyname interfaces, and dynamically loaded it as a shared library system wide. It worked because while most of the same code paths were called, the buffer overflow was only reached when using getaddrinfo directly. Hopefully that company has since upgraded the version of glibc in their firmware. But at the time it made sense because the hack was proposed, written, tested, and queued for deployment before the people responsible for maintaining glibc could even schedule a meeting to discuss the process of patching and testing, which wasn't normally included in firmware upgrades and nobody could remember the last time they pushed out rebuilt binaries. glibc was so old because everybody was focused on switching Linux distributions, which of course took years to accomplish rather than months.