Alpine has Sable, and you can also compile your own OpenJDK (if it doesn't have it already). There are plenty of reasons to use Alpine and just as many not to use it, but lack of a JVM isn't one of them (Pretty much same with Docker- it added nothing of apparently value to me more than that LXC did (or BSD jails like someone above me mentioned), but I'm sure it provides value to some people.)
at the very least, it's probably not worth spending too much time on, because you'd get better optimisations from doing other things