Yes I'm sure the Danes are wishing they had purchased their fifth generation fighters from China or Russia instead.
It's electronic warfare capabilities have reportedly surprised Nato pilots in exercises before.
Maybe a cooperation with French (Safran) or British (Rolls Royce) industry could remove their reliance on the Americans? (Not suggesting overnight but over the next 2 - 7 years.)
Also, they could have bought European planes (Rafale).