If you live in a European Union country and move to another, is there any reason to change your citizenship?

If I compare it to the US and our 50 states, plus DC and some other territories that belong to us, we can move anywhere in the US. There are requirements for us to become a resident of our new state when we move. Does the EU have the same thing from one country to another? Is there any requirement or benefit to becoming a citizen of the new country you are living in if you live there a long time?

In the US there are benefits to becoming a citizen if you come from another country, especially if you are a spouse and never have worked in America. For instance, my inlaws are residents in the US, we call it having a green card, and my FIL having worked here over ten years is entitled to social security. They both are entitled to Medicare (senior health care) but, my MIL only has doctor visit coverage. No hospital coverage and no prescription coverage. My FIL has all coverage. If they become citizens they both can have full coverage.

Also, only citizens of our country can vote in elections, I assume it is the same in Europe? If you are German and live in Spain, can you vote for politicians in Spain?

What are the advantages and disadvantages to changing your country citizenship within the EU? What are the requirements? Does it never come up, and I am overthinking it?