Looking on the RS Components website it looks like a RGB LED will draw about 0.09 watts and a green LED about 0.06 watts. This may not be correct for the exact components they have used and I may have misinterpreted forward current as I am not an electrical engineer (although I did study some electronics a long time ago).
Our gen 1 batteries have one RGB status LED and four green SOC LEDs. That infers the LEDs for each battery will use around a third of a watt. Our gen 1 inverter has 16 grid/solar/demand/battery flow LEDs and one "lightning bolt" shaped status light. Assuming that the status light actually uses two LEDs or a larger single LED of equivalent wattage to two single LEDs that gives an assumed draw of circa 1.62 watts.
I recently had a battery drop off the system and needed to call GivEnergy support to get it back online (thankfully I noticed quite quickly). As part of that call I was asked questions about the state of the lights on each battery.
The obvious problem is that if all of the lights are off then they cannot contribute towards such fault finding. The battery did not initially come back online after restarting it, so it's perfectly possible that there would be no way for a user to reliably re-enable the lights in the event of a fault to aid such fault finding.
If the fault is a communication issue then it obviously wouldn't be possible to re-enable the lights via the app or portal, so at the minimum they would need to default to on after a restart until explicitly switched off again. Restarting a battery is relatively simple (as long as it is willing to play along) but I believe restarting an inverter means isolating from AC, DC and panels and waiting a period of time for residual power in the system to die away, before carefully reconnecting everything in the correct order. Getting the order wrong can, I believe, cause damage.
This seems like an awful lot of work (and potential risk) to go to in order to save at best maybe 2.5 watts for a two battery system.