Why aren't major stock sites offering direct bank deposit in local currency?
e.g. Dollars in USA, Euro in Europe and GBP in UK and so on?

International stock sites surely have lots of money in many different currencies.

This could save a lot of money for both the payer and the payee, since PayPal, Skrill and Payoneer have fees for transations, plus (quite high) fees for currency exchange.

Am I missing something?

You are missing the insane banking fees. Its not as easy as you think. Thts why they all use PSPs

Even if they paid all European artists from a single European country, avoiding double forex?

This seems like a bad workflow to me:
- European buyer pays in EUR;
- Agency pays through paypal in USD (EUR to USD commission plus normal paypal commission paid by agency);
- Artist withdraws in EUR (USD to EUR commission paid by artist);

We (payee) can easily lose 4% in this; the agency (payer) will lose less but still lose.

Many banks offer free bank transfers within EU.
Shutterstock even has an office in Berlin now.
German and Scandinavian stock agencies (low earners, unfortunately) offer free direct bank deposit, so it's feasible at least within the EU.

But since no one it's doing, you may be right.