The first is that getaddrinfo is specified by POSIX, and the POSIX evolve very conservatively and at a glacial pace.
The second reason is that specifying a timeout breaks symmetry with a lot of other functions in Unix/C, both system calls and libc calls. For example, you can't specify a timeout when opening a file, reading from a file, or closing a file, which are all potentially blocking operations. There are ways to do these things in a non-blocking manner with timeouts using aio or io_uring, but those are already relatively complicated APIs for just using simple system calls, and getaddrinfo is much more complicated.
The last reason is that if you use the sockets APIs directly it's not that hard to write a non-blocking DNS resolver (c-ares is one example). The thing is though that if you write your own resolver you have to consider how to do caching, it won't work with NSS on Linux, etc. You can implement these things (systemd-resolved does it, and works with NSS) but they are a lot of work to do properly.