Incorrect. In PoW, the network is secured by hardware, so the owner of a majority of coins is irrelevant. To anticipate your argument: yes, if one person decides to buy the majority of coins and attempts to destroy them by "dumping" that will drive the price down and reduce the economic incentives to mine. EXCEPT, that as fewer people mine, difficulty adjusts and mining becomes less expensive relative to rewards. Not only that, but as that paper points out, the cost of operating mining rigs is marginal (especially with difficulty adjustments).
No I didn't mean it like that. In POW you can buy half of the hash network and have the same argument of "no cost" 51% attack if you don't count money as cost. And thats absurd.
That's true, but buying that much hashpower would require a non-trivial investment. Not only that, but it would be very difficult, if not impossible, to acquire that much hardware due to manufacturing time and relatively small product pipelines. Such an accumulation of hashpower would have to happen in secret, which is also unlikely, because if it became known, the network could easily embrace a hardfork to change the PoW algo.
I guess the point is that theoretically PoW could be attacked, but it would be vastly less expensive to attack PoS. In fact, the greater the attacker's credibility, the cheaper the attack would be.