The cynical in me attributes this presence of Java in enterprisey applications to the huge piles of documentation, flows, UML diagrams, the piles of servers, ESBs and Oracle databases, along with the priesthoods that keep all that in place and up to date.
Reading that pile of documentation and interviewing the hordes that tend to the application are much more work than it would take to write a more modern version of whatever that does with 1000 lines of Perl (or Ruby, or Lisp, or Python, or Erlang, or Haskell).
It's not as much as Java did something right, but more like we did too much around it.
Disclaimer: I am currently struggling with a web application that's little more than a CRUD, but done with what I call "framework bingo" on top of a complicated network of servers, with dedicated Mule feeding Elastic Search servers where a simple CRUD (even the one that comes free with Django apps) feeding a static file system would offer better throughput and easier troubleshooting than the huge pile we see there.
According to Moore (Chasm guy), new technologies tend to get standardized on by big organizations. Adopting it in the first place was hard enough, and they want to put off doing it again for as long as possible. The infrastructure and dependencies (those huge piles) are a big part of why it's hard to change. Some are important and necessary dependencies that are expensive to change no matter what. I think this is characteristic of the enterprise.
Back-compatibility facilitates this postponement of change.
I daren't be an apologist for that webapp (esp since I don't know anything about it and I agree with you anyway), but my inner contrarian pipes up with Joel's essay on rewrites
(http://www.joelonsoftware.com/articles/fog0000000069.html). Though it sounds like there isn't even a grain of truth with respect to the architectural decision.
I believe this specific application can be rewritten in a week or so. If we factor in all the resources that had been dedicated to making small changes and the disproportionate amount of effort dedicated to make sure those small changes didn't break everything else, I'd go with a rewrite even if we kept the whole damn thing in Java, just with a saner architecture.