score:4
Whether you need to go back to Mexico to pick up your passport is entirely up to Italy. Staying too long in Switzerland before you have got any proof of your Italian citizenship does seem risky. But if you really become an Italian citizen shortly after entering on your Mexican passport (or perhaps already are one) and are able to pick up a passport or ID card in Italy, I don't see why it should be a problem.
Note that no matter what your citizenship is, there would be no record of your leaving Switzerland for another Schengen country. What counts is the time you spend in the whole area and it is enforced mainly by looking at the stamps in your passport. So if you show up at a border checkpoint (entry or exit) with only a Mexican passport and a dangling entry stamp older than three months, you could get in trouble. Ditto if there is a police check for some reason (it can happen in some countries).
But if you do get your Italian passport or ID before the end of the three-month period, this should not be relevant anymore as you have the right to be in the EU and can use the Italian documents to prove that, leave and reenter whenever you want.
Importantly, most people who get a citizenship by naturalization (probably not your case but I think the example is still relevant) are already present on the territory of the country in question. Once they get their new citizenship, they simply don't need their existing visa anymore but there is no requirement to leave their new country of citizenship, let alone the whole EU.
The main issue with your plans is that you would be leaving to Italy or Switzerland hoping to get the new passport in a timely manner but could find yourself staying there with no documents because of another delay in the process.
Upvote:2
In practice, if you acquire EEA citizenship whilst in a member state your existing visa becomes redundant. You do not have to leave and re-enter FOR IMMIGRATION PURPOSES.
If you lose your Italian passports and need to rely upon your Mexican passports, there's a potential vulnerability if you cannot show compliance with the terms and conditions of your visa(s).
Secondarily, some countries have tax and pension regulations that involve day counts in foreign locales, you may need to check with tax authorities to see what the impacts are (if any) for your particular case.