It probably would've caught on more/sooner on the desktop if it had adopted a native-look-and-feel GUI toolkit earlier rather than later. Hopefully a WASM reincarnation of Java's cross-platform goals will prioritize that sort of look-and-feel integration.

Specifically, if all we knew about user-facing Java was that most Android app are written in Java (or something that differs from Java only enough to try to avoid infringing the intellectual property rights of Java's owner) then we would expect many cross-platform user-facing apps to be written in Java.

But we have no need for such indirect evidence because we can directly count the cross-platform user-facing apps that are written in Java. You mentioned one, Minecraft, and I will add Eclipse, IntelliJ and its derivatives and Jin (a "client" used to connect to the Free Internet Chess Server and Internet Chess Club). Since I know how hundreds of user-facing cross-platform apps are implemented, and since four out of hundreds is not much, I stick to my claim that Java never caught on for writing cross-platform user-facing code.

Depends on how you define "platform". Android apps certainly run on multiple architectures (mostly ARM, but also x86 and MIPS). They also run on non-Android operating systems (namely: ChromeOS; theoretically-speaking, other operating systems could run Android apps, too, so long as Dalvik runs on those operating systems, though unfortunately this is not the case for most operating systems).

And sure, we can provably claim that Java didn't "catch on" compared to the sheer volume of user-facing programs written in C or C++, but by that logic macOS didn't "catch on" compared to the sheer volume of user-facing computers running Windows (which might indeed be true depending on how you define "catch on").