The reason I hadn't ever speculated on this point is simple. I'd seen Dutch-brewed Stout as soon as I came to live here. It wasn't very common. I only really remember one brand, van Vollenhoven, brewed by Heineken. I drank it a couple of times. No tasting notes, I'm afraid. Just a few raw stats from my website
Van Vollenhovens Stout
6% ABV, 16.1° Plato
Bottom-fermented stout. Named after an Amsterdam brewery bought by Heineken in 1941 and closed in 1960.
Bitterness 33 EBU, colour 180 EBC.
(Pretty sure I've got the closure date of van Vollenhoven wrong I think it was much earlier than that, just after WW II. And it might have been 1942 when Heineken and Amstel jointly took control of van Vollenhoven.)
It wasn't a particularly memorable beer. I don't think many tears were shed when it was quietly dropped. Soon to be resurrected, luckily, after Heineken sold the rights to the name. It was first brewed under licence at De Schans in Uithoorn. It currently resides at Poesiat and Kater in Amsterdam. A lovely beer, which you should try if you have the chance.
Getting back to the initial question, the simple answer is: because they had been brewing Stout in Holland since the 19th century And it followed the same course as in other parts of Europe. Initially, Stout (though sometimes called Porter) was imported from Britain. Locals brewed noticed that drinkers would pay a premium for it and decided to get in on the act.
I doubt it was ever brewed in enormous quantities. But, as the profit was larger, it was worth a brewer's while.
Other British styles which were imported - such as Mild Ale and Pale Ale - never really caught on. Only Stout. Though not a big seller, it was mainstream enough to figure in price-fixing arrangements.
Sometimes the quantities were tiny. Amstel sold just 88.26 hl of Stout in 1939, a mere 0.03% of its output. Bizarrely, all of it on draught. In the 1950s, Heineken brewed production batches on its pilot plant. But they did still continue to brew Stout, these big Lager breweries like Amstel, Heineken and Oranjeboom.
Quite nice that there's a just about uninterrupted history of Stout brewing in Holland. They're much more common again now. Butcher's Tears alone brews dozens of the things.
Why were the Dutch brewing Stout in the middle of the 20th-century? Because some Dutch drinkers got a taste for the black stuff in the 19th century.