Well, to be fair, there was a vertical separation of powers too. (It's just that by making the Senate a sort of super house-of-representatives we stripped States-as-institutions from the federal government.)
(That and the frighteningly pervasive view that the federal government is, in all cases, superior to the States.)
They considered and immediately rejected a popularly derived senate, and would barf at the thought of six year terms for elected reps.
Also, check out Article I Section 10. These are the powers relinquished by thirteen nations to an umbrella republic of their creation. They didn't give up a single power until their presence in the senate was assured. The constitution was entirely contingent on a senate of the states.
The constitution acts on both the people and the states, so both were represented in the law making body. It makes as much sense in our system to boot the people from congress as it did to boot the states . . . no sense at all.
The 17A left behind a federal constitution without a federal government.