And yes, I can understand that for some people the inability to easily transfer and collect those conversations is a problem, but for many people (imo probably more people) the ephemeral nature of these messages is a feature, not a problem to be solved. At least that’s why I use Signal over Messenger, for example.
I have this problem; most Android apps send background notifications via Google's Firebase Cloud Messaging instead of rolling their own services. (Signal is an exception to this.)
So, if you're unwilling to use Google Play services (or us an OS which doesn't support it), you're fucked and will not receive background notifications. The primary reason I use bridges with Matrix is not to unify my messaging experience into one app, it's to get notifications on my phone.
I don't know about WhatsApp, but at least Telegram and Threema can fallback to polling if push notifications aren't available. With polling there is of course the trade off between battery usage and message delay, but you shouldn't miss any messages.