Sending money to the intermediary is still essentially free. The likely incorrect assumption here is rather: that it would do any good in this case. Because that only works when the intermediary has agreed to do anything other than facilitate wire transfers (with the beneficiary account number and cost schedule specified!). They would say so in the instructions (e.g. a note on how the SEPA reference field should be filled), if that were the case.

SCT is not contingent on EU or Euro participation - SEPA membership is distinct from those. That is how Iceland, Norway and Switzerland can reap the benefits (the latter not even EEA member, though effective treaties are now somewhat similar). As long as an US bank has a correspondent branch/account/partnership/whatever inside SEPA, they can make it almost free to receive money via SEPA, and then possibly still save on currency conversion and transaction cost as they clear in bulk across the pond.