Flying to AMS this argument makes sense, but not for LHR or BRU. The OP isn't complaining about high fares in general, he's complaining about DL's fares being out of line with the rest of the market.
AA, BA and DL all publish business cabin fares NYC-LON for ~$2,000 r/t that have no advance purchase requirement. AA, UA and DL have similarly priced fare w/o adv purchase to BRU. The great difficulty is summer season availability.
There
are low fares to be had between NYC and LHR/BRU/CDG/AMS on DL/AF/KL-coded non-stops in the business cabin - even in July - but one needs fair skills with a search engine. ExpertFlyer is useful too, to outline adv purchase and minimum stay requirements because it's a waste of time to look for things that aren't going to be there.