All the document and its regulation do is say, "if you impose entry requirements based on vaccination / testing / recovery, you must accept at least these types of vaccines / tests / recovery specifics and you must accept this document (if genuine) as proving what it says, and all of this on a non-discriminatory basis regardless of nationality or place of occurrence." The document itself is never made mandatory by the EU and alternative proofs for entry to a member state must be accepted.

(Why do I say "document" instead of app? From the user perspective, you can print it on paper, present it as a PDF, or use one of many interoperable national apps among other ways to present it.)

So, the restrictions you're unhappy about are imposed by countries in reaction to COVID; the document we're discussing just sets some minimum allowed level of ease in satisfying national entry requirements.