You have ignored the implications of the variable k and note the equation fails to consider capital costs. Chomp on that for a while, as I need to step outside for 3 hours. You will soon come to realize that the above equation is nonsense.
k is the number of double spends an attacker attempts to pull of at the same time. In theory it can mean there is no upper bound for when it is safe to accept a transaction in bitcoin because, under a theoretical elastic block size, the attacker can attack an infinite number of merchants at the same time. However in practice the author of the paper assumes a k of around 4/5 (can't recall exactly), because there is a limited window in which the attacker can pull of his attack. There is a way around this problem with k, but its for another discussion.
In your system, however this is completely unbounded and there is no way to place bounds on transaction acceptability because PoW is not being valued, therefore the recipient can never tell when it becomes unprofitable for an attacker to try and double spend your transaction.
The capital costs argument applies equally to all PoW coins, I don't see the relevance?
edit: am I the only one who sees the irony in you calling a critical equation 'nonsense' from a paper which you yourself cited as being 'bitcoin 101'?