I have found an answer for this by following this advice:
https://code4ward.net/2011/10/10/service-owner-notification-for-distributed-apps
In short, we shouldn't override top level Health Entity monitor, but rather "All Contained Objects monitor".
I did this for "All objects of another class: User Created Distributed Application" and now all my DAs alert on health state change.
One of the caveats is that the rollup is "Worst Of" and there is no way to configure it further, but it works for us at this stage.
We have further scoped this alerting in subscriptions so proper owners only get the alert.
Hope this will help someone in the future, although it would be good to see how to have better control of health rollup.