A power bank is just more batteries, so using slightly larger batteries in the first place makes more sense.
A suitable power supply can be used for charging - but needs external power. (It's a battery charger, in other words).
A small generator is the only thing you could use to charge & run indefinitely, making it in to a hybrid.
You should not have to disconnect the batteries to recharge - the generator can charge while they are in use, as long as it provides more than the average load power and the batteries are properly monitored.