It's useful to keep it plugged in because it has bypass charging to use power directly from the charger without going through the battery. It shows the shield icon while doing this. The battery will last even longer if you leave the device plugged in since it's avoiding using it.
As also asked in the dedicated "New Battery Bypass feature in GOS?" thread:
Does the battery bypass require the use of a USB-C Power Delivery charger with PPS (Programmable Power Supply) feature support?
Or does it work with any USB power source?
Samsung devices apparently require the use of a USB-C Power Delivery charger with PPS feature for the battery bypass (called "Pause USB Power Delivery" on Samsung devices) to work.
In the following random example video, the power meter seems to indicate that the phone is essentially constantly drawing around 8 Volts from the PPS power supply when using the battery bypass mode:
https://www.youtube.com/watch?v=YvAWT-zIWhQ
Maybe this is because batteries typically output around 3.7 to 4.2 Volts and therefore maybe a phone still requires this voltage range when bypassing the battery. Maybe in this case the phone has a built-in voltage step down converter to half the around 8 Volts to around 4 Volts to then constantly operate at around 4 Volts in the battery bypass mode.
That maybe could explain why a PPS compatible USB-C power supply is required for the battery bypass. Because only PPS compatible power supplies are able to output variable and dynamic inbetween voltage values, whereas non-PPS power supplies are limited to fixed voltage values such as 5 Volts and 9 Volts for example.
Maybe someone can clarify if Pixel devices also require a PPS compatible power supply for the battery bypass feature to work.