Outside of a proxy, is there a way to log, or view network calls apps, services, and processes are making/have made on iPhone and iPad devices? For forensic analysis/malware hunting. I’m aware there open source frameworks and apps where you can tail the live syslog, but the log level isn’t granular enough.
If this is an app you're developing yourself, you can use Xcode and the accompanying Instruments program to setup a Network tracer. From there you can see for example all the HTTP calls that your app makes.
Another option is various forms of proxies and VPN software that you can use to intercept, log and view network traffic. However, you state in your question that you do not wish to use these.
Apart from the above, there's no option for intercepting all network activity made by apps, services and processes on iOS devices that are not jail-broken.