Appeals Committee. Disputed situations in tournaments.

I believe that the rules for this particular game scenario are perfectly thought out...

Well, if they are, in your opinion, perfectly thought out, then quote the rules – the very passage from which it directly follows that
A player with archers must surrender in battle as soon as the player with skeletons indicates this to them.
(or some other passage in the rules, thanks to which the situation is unambiguously resolved in your opinion)

Technically, the owner of the skeletons can simply hand over control to the computer and go to sleep...

I'll just wish you technical luck in pressing the autobattle button in a battle against a human.
By the way, I agree that if this were possible, there would really be no controversial situation. But here's the problem – the button doesn't work in a Human vs. Human battle.

Nevertheless – it is precisely this argument of yours – although it doesn't work in practice – that specifically convinced me that the decision should be exactly this – the archers should retreat.
But I still don't agree that the rules are perfectly thought out – and I still suggest finding a quote from them that unambiguously resolves this situation.