From experience, generally you can get through on the phone quicker as a Flight Club member - however, with easyJet I think its the whole digital side they are lacking. Your ‘profile’ doesn’t know if you’re flight club or not, your can’t even see what your membership number is through the profile.
For something like this, whether you pay for easyJet Plus, or a Flight Club member (remembering you have to fly a decent amount of times to qualify) - I know they want to move away from physical cards, but there’s nothing stopping them having digital ones.