Who is "Everyone"? EU is trying in various ways to reduce tariffs, like (biggest example I know): Mercosur, to quote "both the EU and Mercosur will gradually reduce import duties on 91–92% of exports" (https://en.wikipedia.org/wiki/EU%E2%80%93Mercosur_Partnershi...).

Of course European farmers complain (they will get competition and potentially lower quality products), so yes, some people like the current tariffs.

Behind every tariff there will be an interest group. If you are producing X in a country and there is an import tariff on X you are happy. If you are buying X you are not happy.

There can be strategic industries that you want to encourage, but the issue is if tariffs are applied with a plan or not. Opinions might differ on this one but history will tell.