So assuming the app isnt E2EE then there would be many ways to read message contents, for example if the subpoena your email provider, or SMS provider. Google play store and apple store again also already have all the details of what apps you use, how often you update them or when you removed them.... There is just no benefit to using push for this kind of data gathering, there is always one or more much better ways of obtaining any of this data... wanna know when a woman left the state to go to health clinic? Cell towers. Husband suspected of murdering wife and you want to know what dating apps he used? Google play store has logs of every dating app they joined, and all those dating apps will gladly hand over chat logs and other data to proper authorites when asked nicely... And its not like the pushnotifications themselves are just open air unencrypted broadcasts anyone can monitor, Law enforcment at the very least has to submit the requests to google and apple anyway, so why would they care about push notifications when they can get access to a suspects entire cloud storage and emails?

I'll bet whats really happening here isnt even that cops are "super interested" in push data, but rather they realized that its one of many forms of data that they include when make a request. I'd bet tey also grab any kind of "fitness" related data , and things like your advertising preferences too, because why not? Investegators don't usually go around asking for just the bare minimum they need to incriminate someone or prove an allegation, they just fill out the data request form and check "all of the above".

Go look at how many different options google takeout has, and imagine they probably have a few bonus ones just for law encforcment, Push notifications is just a drop in the bucket in terms of the data that we're all giving away freely by depending on the duopoly of google/apple for all our mobile communications.