The whole point of WEI is that the site can choose to block any combination of browser and OS they see fit, in a reliable way (currently, browsers can freely lie). CURL and friends will almost immediately be branded as bots and banned - that's the stated objective.
It is more severe than that. The design favors a whitelist approach: Only browsers that can get the attestation from a "trusted source" are allowed. Browsers that cannot, don't.