This one confused me. The obvious reason why you don't want the whole working set of your database in the app server's memory is because you have lots of app servers, whereas you only have one database[1]. This suggests that you put the working set of the database in the database, so that you still only need the one copy, not in the app servers where you'd need N copies of it.
The rest of your post makes sense to me but the thing about keeping the database's working set in your app server's memory does not. That's something we specifically work to avoid.
[1] Still talking about "non-webscale" office usage here, that's the world I live in as well. One big central database server, lots of apps and app servers strewn about.