Like you, I don't think a parliamentary system would make much difference. It would still be the same people being elected. And whether they're in the opposition or in the majority, they don't seem to be able - or willing - to accomplish much.
Comedian Lewis Black once said that "the Democrats is a party of no ideas, and the Republicans is a party of bad ideas!"

In Finland^[1] we have a semi-presidential system, somewhat akin to France, and the power of the presidency is a constant source of debate. Its power has been significantly reduced in recent years, but there are still frequent clashes of jurisdiction between the parliamentary government and the president, particularly in foreign policy, which is the primary field of concern for the president.
(Of course, Finland has proportional representation, with no party even daring to dream winning 30% of the seats, so coalition governments and consensus are a must.)

^[1] Yes, I have an amazing ability to reduce absolutely everything to Finnish analogies.

"The basis of optimism is sheer terror" - Oscar Wilde