Financial markets are positive-sum.

Not necessarily. First, it depends on the market. Some are zero-sum, and about others one can say that they are NOT zero-sum, but that's it. They might be negative-sum or positive-sum, depending on the circumstances.

If you just buy a bunch of stocks and hold onto them, on average you'll outperform cash.

That also depends. Average over what? Which countries and what time periods?

If you buy a stock A at price X, somebody must be selling you stock A at price X.

If buying turns out to be a good deal (that is, the discounted dividends Y you collect from holding stock A are greater than X), then selling must turn out to be a bad deal: if the other party held stock A they would have collected the profit Y-X that they forfeited to you. Your gain is their lost profit, therefore the market is zero-sum between investors. Add transaction costs and it becomes negative-sum.

This analysis is simplified by the fact that I didn't take into account risk aversion and the fact that different parties can discount future utility in different ways (different discount rates or even hyperbolic discounting). But I suppose that when it comes to collective investors such as mutual funds or banks, these parameters can be considered to be roughly the same.

The stock market is not (necessarily) zero-sum or negative-sum as a whole, since money is transferred from companies to investors each time dividends are paid, but the way the investors slice the cake between them is negative-sum.

Yes, but taking into account survivorship bias, there are some actively managed funds that do do consistently worse than the market, and eventually fail (and are replaced by other funds that do so)