If a person says they’re Jewish, they’re believed, for the purpose of aliya l’torah, etc.
Rambam says we only investigate for the sake of chupah v’kiddushin.
Your ideas sound draconian, There are also many cases where people are observant but they’re rejected because the converting rabbis are politically incorrect- for instance, R’ Karelitz’s converts in Israel are not accepted and cannot attain citizenship.