Why can't price level be negatively correlated with money demand?
You're supposing the amount of money held for transactions by players is arbitrary. This may be true if you look at an individual - I typically withdraw fixed amounts of money when my purse starts feeling empty - but is not true on average and in the long run.

But cash (in the wider sense, money on regular bank accounts count toward this) is also held by companies and foreign countries.



Even if you feel like discussing the rationality of the average person, you cannot discuss the rationality of the average money holder: the opportunity cost of holding too much money may be negligible for an employee with low savings. But it it isn't for a big multinational or a multi-millionaire that wants to stay richer than his neighbours in Beverly Hills.

Consumers are also retailers, at some point, so you cannot suppose the price rise affects them in the way they buy less goods. A potato producer still produces 1kg of potatoes after a price rise, only they are worth more and he need more money to buy carrots. The money demand increases because there is less money available for the same goods. This is a very different situation than a productivity drop, in which case the money demand would decrease.