I'd love to have a way to monitor signal quality for my favorite channels, especially when I'm not recording. I'd be happy with an estimate of how often symbol quality drops, and what the average signal quality/strength are. I go for long periods with no issues, then get occasional pixelation, looking for tools to help troubleshoot.
You can view this info on the tuner's web UI. It is also available in the hdhomerun_config_gui app. (For the app, you can build it from source for Linux and macOS; some Linux distros have prebuilt versions, it ships with the Windows software, and used to ship with the macOS software but it is no longer included.)
For logs over time, you may want to script something from a cronjob.