I don't disagree with any of this, but there is a logic to it all the same.
The parties are divided because the people themselves are divided. Perhaps astonishingly, MPs are, even now, still by and large representing what they think their constituents want. And in that sense, the system is functioning as intended.
At least with Leave/Remain constrained within Labour and the Conservative Party, the two sides still have to talk to each other.
Whereas a more coherent partisan reflection of the Brexit divide would mean permanent civil Cold War, like in America, where neither Party even attempts to represent the enemy traitors. We should think very carefully before we deciding that's the answer to the current impasse.
In any case, Labour has made clear that although they might not deliver the Brexit that you or anybody else wants - because who could? - it will undoubtedly be a softer Brexit than what the Tories can agree upon.
And, more importantly to me if not to you, Corbyn is also the only national politician with any longer-term ideas on how to resolve the underlying cultural and political crisis, by prioritising the deeper causes of Brexit - namely austerity (centrist liberals' original 'sick of experts' sin) - rather than keeping everything else the same and patching up the effects.