Of course it doesn't. A little thing called the Constitution has that covered.
I don't know why you think that it would take amending all 50 state Constitutions. Did they amend them when the 17th Amendment was enacted? I've never researched it.
Why do you think it would take 3 different Amendments to enact Congressional term limits? It only took one to enact Presidential Term limits.
There are arguments the 17th should never have happened but am not sufficiently enough versed on the issue to advance an argument of substance. It wasn't a restriction on the people though it gave them more power over elected officials.
The President is elected by all the people of the several 50 states etc. Congress members elected by the individual states
he 1st amendment protects freedom of speech, political speech by way of elections also protect right to petition the govt through chosen elected officials.
10th amendment should be self evident
11th Immunity of states from suits from out-of-state citizens and foreigners not living within the state borders. Lays the foundation for sovereign immunity
I suppose it is possible term limits could be done with a single amendment . just giving the federal govt more power over the people.