I'm Italian, used to our president mostly approving laws, commanding the armed forces (in theory, not in practice) and very few other things. And the best thing about our president is that it gets elected by the parliament requiring a very sensible majority. Thus pretty much all parties need to agree on one and they end up electing non-political figures (or politicians that have demonstrated high level of trust regardless of their party).
I think our system works great to be honest, and I already see the huge problems having an election-based president in Poland has with the government and president being from different parties and clashing with each other and the president vetoing for years a democratically elected government just to stir trouble.