There was an income tax before 1913. One was instituted to pay for the civil war. There was also a variety of other taxes that existed from the very beginning, so it isn't like the notion of the government levying taxes to perform its duties is somehow new.
The major difference between now and then is that the government is now given a larger list of duties to perform that requires a larger tax base. The argument about the size and role of government has always been going on and will continue to go on, but it wasn't won in 1913, nor was it won only at the federal level. It was won and continues to be won at every level. Look at state and local governments, for example, and they will look much the same as the federal government: relatively large bureaucracies with an expansive set of duties and a substantial tax collection apparatus (sizable debt problems in many cases as well).
It sounds like what you would really like is a libertarian government (small, limited, low taxation), but there aren't any libertarian state governments either, so even if that tug-of-war had more action (due to state elected Senators) neither side is libertarian, so I don't see how there'd be a libertarian outcome.
It might shift some of the size and taxation from the federal to state level, but I am skeptical that it would diminish the overall size and taxation of the total government.
In fact, it is entirely possible that a greater tug-of-war between states and the federal government would actually make things worse. The notion that states would hold the reigns more effectively or responsibly is a pretty major assumption, in my opinion. Fifty horses or one giant elephant doesn't necessarily matter. Ultimately it is the people who need to have the reigns by being active and informed (we tend to be neither).