The filibuster makes this kind of 'control' moot. You need a filibuster proof majority in the Senate and a majority in the House to actually get anything done (and the Presidency, to not veto). 'Control of half of Congress' when that half is the house, is meaningless.
That applies equally when each party is the filibuster-sized minority in the Senate.
And: if Senate majorities really want to pass something, they can change the filibuster rules – and have, for some topics.
Otherwise, the filibuster is maintained out of tradition, courtesy, and its usefulness as a change-of-control 'debounce' mechanism – as well as providing a convenient excuse for posturing more and doing less, as Congress is wont.
Still, in other eras, Congress was able to move compromise legislation forward. Recently, Congress has been unable to – both parties, no matter the relative control. Any belief that it's only "the other guys" is partisan myside blindness.
