My thought was that the caps give up when they got hot, which leads to fouling the plugs.. But I could be wrong :-)
To put it gently, you are, imo.

The coil output circuit is a loop, one lead to a spark plug through head to other spark plug and then back to the other coil lead.
Along the path are two spark gaps of about .025" each (.050" total) as well as inline resistances to help smooth and extend the spark pulse duration and limit the spark current enough to reduce the spark erosion of the D7 plug's hotter heat range (which extends their life).
The stock bike uses a 10K resistor in each plug cap for a total loop resistance of 20KΩ
The cap's resistors can go bad and if you are reading open circuit, they can still work ok, even if they aren't ideal. It only takes a plug cap broken resistor gap of .001" to make them read open circuit. But, adding that much gap to the loop circuit won't make much difference in operation. Over the long term, the arcing inside the plug cap will erode the that gap even larger. But, the symptom is misfires, not plug soot fouling.
Btw, my local Honda dealer recommends me buying 1K ohm caps and NGK D8EA which actually was the setup i bought the bike with. Why does he say that?
Almost certainly that's what he has on hand to sell you. Most of the other SOHC4's of that era use D8 heat range, so he stocks what is most popular and moves faster off the shelves.
I think NGK stopped making the 10K plug cap option due to low demand. So, they are now pretty hard to find. Many people assume resistance is a bad thing and try to eliminate it, which is probably what led to the 1K stocking popularity. Few people understand how electricity works. But, 1KΩ plug caps would allow the dealer to sell you replacement spark plugs more often as they would wear out faster. They like to see you often when you are paying.
To approximate what Honda did originally for your bike (without locating 10KΩ plug caps) you would need 5K plug caps and use resistor plugs (5KΩ each), in order to restore the 20 KΩ loop resistance the factory delivered.
Definitely try a new/ clean air filter or operate without air filter to see if the plug fouling abates. Your call about how dusty/dirty you normal air quality is.
Are your carbs stamped 649? I don't know if Denmark got that importation variety along with the air filter restrictor inlet. If so, that will add a new wrinkle to the situation.