Bigger battery = more amps = controller can draw more amps = more power delivered
Wrong.
It means more power CAN be delivered.
IOW, it means more amps are available. If you have a billion amp battery and only draw one amp, the power delivered is still one amp times the battery voltage but for a MUCH longer time. Works out much like KWH. Cannot have too much, just do not use it, unless needed. The need does not change with the battery, but with the load.
You can never have too much amperage in a battery. Not for anything. It will not change how much current is being drawn, wattage used stays EXACTLY the same, you simply have more available. Having more KWH available doesn't mean it must be used, Same with SUPPLY amperage. Voltage is different, as too much can destroy stuff. So can too much current form the LOAD, not from what's available in the battery.
-Don- Reno, NV