Does it also mean that double spend is allowed as if you have 51%+ mining power, you can do whatever you want?
Everything is allowed. That's fundamental in the "trustless" world. It is a Darwinist fight.
If not, then you need only to put in sufficient safeguards so that any mischievous action is difficult enough for it to be able to be taken to court and justice, and you wouldn't need to spend 400 million dollars a year on wasting PoW on bitcoin for instance. Much less PoW would be sufficient to limit the number of attacks to a reasonable number so that "justice" (whatever power game THAT is) can handle it.
It is the difference between putting a lock on your door to make life more difficult for a burglar, but the real protection against burglars is the law and police, on one hand, and an old sea pirate hiding his treasure on an island in the Pacific, with no legal protection at all.
That is right. You can ask for the 400 confirmation instead of 6 confirmations to determine a transaction is valid.