It's operator decision (docs here) and why "running a node" that you fire & forget doesn't help the chain (though it may help the network if there are many nodes synching - like seeding a torrent.)

Doing anything automatically in this case means that the chain with the most work wins, so the attack you're afraid of would always win within the window then. You need humans in the end: bitcoin isn't automagic internet money because consensus is between humans, not software.

Some miners would. But to overtake in the way you described you need a whole lot more than everyone else. If that happens we'll have big trouble, but no one will revert my transactions because my node will reject these double spends.

However, this is why we're saying that running an economic node is meaningful. Miners have to mine what economic nodes are willing to accept as valid, otherwise their block will be rejected, and that means losing income (especially when income is under pressure, then it becomes even more important that your block doesn't get orphaned, because margins will be tighter.)

After all, like me, you will not take kindly to someone reversing your property either.