Why would I automatically share usage and diagnostics data?
can I have access somewhere and see what Google is collecting about my own usage and my own battery performance? 


Yes. Click on My activity to see what information is collected by Google regarding your app activities (if you didn't disable it). The data is just about how many times and when you used an app (unless Google chose not to reveal all the data captured). I don't know how this can help in improving app stability or performance

What it does with this information is not transparent and I never saw any information being recorded about your battery statistics

If you click on the hamburger menu and go to activity controls, you will see what it benignly tracks with seemingly useful goals (if you missed the sarcasm , see How Google is secretly recording you through your mobile, monitoring millions of conversations )

Bottom line - all your activites are being monitored to improve user experience etc but at a cost. Folks disable these not just because of data consumption but privacy concerns. Smarter folks manage to have minimum Google components - See Android without Google courtesy Izzy

Edit: 


Thanks to OP for pointing out that Google does collect battery information as claimed here. This was new to me but I couldn't find any way this information is available to end users ; developers seem to be able to see it in Android Vitals and maybe elsewhere
Note that you can't disable monitoring, you can only pause ; this means it would be reset to default if you factory reset your device or change your device and could be reset sneakily by OS update or Play Store update. It's better to keep checking periodically if your settings hold