First of all, it would be nice if log-files are text-files we can directly manipulate with scripts. It would replicate logging much better.
Logging more then the existing log-entries would be the next step in my opinion. This includes things like bash history, more actions done on system, dedicated log per binary, etc.
To round that, change the print-function that it writes logs by default, customizable over arguments. I guess logging-frameworks will follow by the community very soon after it.
The log-viewer can still be upgraded aswell to not only show logs, but directly edit them.
Finally, it would change how trace-clearing and hunting can be done.
Happy to hear your thoughts about a topic, which is in my brain for very long time.