So, that is not how sabbath mode I am aware of works. I
think in this case most rabbis would agree with you; I've never heard of a sabbath mode that turns it on after a "random" delay. I think the GP was mistaken.
Rather, sabbath mode is things like... a sabbath mode elevator just goes up and down all day stopping at every floor, so nobody needs to press any call or floor buttons. A sabbath mode oven, what it actually does, it just stay on all day (disabling features that will turn it off if unattended for a few hours), so you can just leave it on at a relatively low temperature all day and put things in and out of it, without starting a fire yourself. (It is starting the fire that is forbidden not making use of it). (In some cases a timer you set in advance before the sabbath is okay though, so perhaps a sabbath mode oven could have a timer you set Friday afternoon telling it to turn on and/or off at some point in the future).
HOWEVER. In general. I think there is a larger point. As someone who does not particularly believe in God, but still has some respect for following disciplines like this: You say the rules are "meaningless" -- but I would say the rules are meaningful only because of the meaning WE give them, the effect they have on us, the meaning we find in them.
If you don't believe in God, that's the only kind of meaning there is, anyway, right? Or you believe everything is meaningless in a kind of nihilism, which is something some people do, but I don't believe it's what most of us atheists do or is the only option.
So the rules of shabbat can be "meaningful" because of the meaning we find in them, because of the _experience_ of following them, which may be an experience that we find meaningful, especially when done with a community doing it consistently. Shabbat is a good example, because I find it to be so, having some experience with observing it in a community; it is a pleasurable and personally meaningful experience with no need to believe in God to make it so. So whether a modification of a 'strict' rule would make sense would depend as much on the effects it has on the practice as anything else.
I don't think religious Jews usually look at it quite this way (although not as different as you may think either); but the Amish, for instance, I think are closer to this. It's not exactly that God said don't use cars so you go to hell if you use a car; it's what effect do cars have on our lives and communities, and do we want those effects, and it might be okay to use a car sometimes in ways that minimize those effects for a greater good (say, an ambulance, perhaps).