UPDATE: Not sure exactly when it happened (I think since Erlang 22) but I can now issue asdf install erlang 22.x.x without having any older JDK/JRE versions on my Macs (confirmed on two). Erlang installs docs just fine while JDK/JRE 13.0.x is the only installed Java on your system.
I also confirmed it on a Manjaro laptop with JDK 13.0.1. So the above post describes some pretty meaningless gymnastics, as of today at least.
Disclaimer: I am using macOS 10.15 Catalina.
