There's no inherent technical reason why the Android activity which currently registering for the ACTION SEND intent filter couldn't also interface with the underlying Evernote API in order to add new tags. The Android OS APIs place restrictions on what is being shared (i.e. text, imagez), not the business logic performed once the app has received it (and the same is true for the equivalent iOS Action/Share extension APIs).
Or to give a concrete example, both Pocket and Todoist have managed equivalent "add new tag" via Share sheet features in their respective mobile apps. Evernote has its own distinct backend infrastructure so it's not a 1:1 comparison as its subject to different tradeoffs to those other services, but it's 100% inaccurate to say that the limitation is OS based.
I agree with the OP that it's a major omission, and such a major use case of the Web clipper should be ported to mobile ASAP.