I'll let that sink in for a moment. Separate flights: from Dubai to Munich, Munich to Washington, then home again home again joggity-jog. Cost of all four flights: around AED4200 per person.
These flights are scheduled for every day of the week, and it stands to reason that it costs the airline exactly the same in landing fees, passenger handling, luggage handling, extra take-off fuel, etc., whether our stopover in Munich be four hours or four days. The only additional costs that I can identify are use of the baggage carousel, and having someone inspect our passports. And these costs are borne by the airport, not the airline. They're presumably funded from landing fees and therefore paid for anyway.
I tried many variations to get a stopover in Munich, but every one of them totalled up at the same cost, to within AED100 or so.
Why, then, does stopping in Munich on the way west cost AED8250 per person? That's almost twice as much money for exactly the same effort. Anyone would think that Lufthansa didn't want people to visit Germany, to stay in German hotels, ride on the German rail network, drink German beer and Glühwein, eat German Wurst, or buy German Christmas ornaments; in short, spend money in Germany.
So we won't be stopping over in Munich after all.