My mental model of truly idiomatic Java already doesn't use new often, and it is then easy to take code which was written in idiomatic Java to remove remaining uses of new; like, idiomatic Java--even the classic stuff--tends to pass around primitives and uses imperative code to manipulate data structures... most algorithms don't really allocate anything other than strings (which are easy to accidentally allocate as those allocations are hidden by the library as opposed to the language, but also tend to be well-scoped in the codebase to parsing logic that should be using more powerful abstractions anyway... and knowing Java developers probably got replaced by XML early in the development cycle, the parser for which you might choose to view as a massive string factory factory ;P). As for the stereotype, it is really important... I added some extended references to my comment, as if you aren't using factory factory factories are you really using Java at all?! ;P. (FWIW, in Execution in the Kingdom of Nouns, two of the examples use new... but almost entirely in ways that feel completely unrealistic to me as someone who did a lot of programming in Java; then the remaining couple allocations I could see being "forced into" would trivially be replaced by a shared instance ;P.)

If you're into factory factories, you should really dig deep into delegation factory factories. There are many. They are a joy to work with as you get to export both interface blueprints and heap allocations to external third counter-parties. Just remember to sign full contract certs before doing anything by wire.