No one is being "punished". It's a matter of politics.
In the European Union, recovery, i.e. natural immunity is recognised, in other countries, it's not recognised for exemption, or is in addition to vaccination, like in the UK. The NHS App won't issue you a recovery certificate unless you've had a full course of a vaccine. They're following different scientific guidance.
An unvaccinated person who has tested positive, is exempt for 6 months. According to the start of this thread, the formerly known as fully vaccinated is valid 6 months just like a person who has never been vaccinated. They're in the same position.
There's debate as to whether "boosted" persons are also included in this 6 month limit, or if its 270 days, which is what's set out by the Commission with EDCC, The Commission may change the validity "On the basis of new scientific evidence on this issue, the Commission may, if needed, propose an appropriate acceptance period also for vaccination certificates issued following a booster." In fact, the ECDC recommended 6 months for the "fully vaccinated" before boosting but 3 months was added as a grace period which is where 270 days comes from. Hence, Italy's 6 month validity is based on ECDC guidance. Member States are free to set validity, they could go down the route of Israel, again, it's politics. There can be no basis in science for boosters to have "no expiry", that's just not what the ECDC is recommending. The only way boosters don't expire is if there are no more boosters and the vaccination programme ends.
With 500k cases in France, I find it hard to believe 500k people are deliberately getting infected or indeed anyone is really going out and licking door handles to get a recovery certificate. Likely it's so rife in the community and the French test a lot. If there's 500k cases, there are many more asymptomatic like the new "Stealth Omicron". Those 500k people I mentioned will posses a certificate on their TousAntiCovid App because France recognises natural immunity.