I think that strobe lights should be recommended but not essential. They're useful on the ground, because if you see a stationary aircraft with strobes on then you are aware that the aircraft is either starting-up or shutting down, and when it starts up you can expect the aircraft to move.
However, strobe lighting doesn't really improve safety on the ground because common sense would advise aircrew and groundcrew airside to stay away from propellers as a general rule, and the responsibility is with the pilot to ensure all persons are a safe distance from the propeller before starting anyway. Anticipation just increases awareness, not necessarily safety.
The only time I've ever noticed strobe lights in the air is when flying at night; but as the OP's LSA won't be cleared for night-flying this is really a poor argument for strobes in this case. More importantly, I'll address the OP's second point:
Originally Posted by Ultra long hauler
It looks nice! (cool, if you like).
Aeroplanes are cool, full stop. Flashy bling to jazz the airframe up are not required, the aircraft will look just as cool without them.
