Yes, Obama could win. He was the leftist candidate in 2008, though that fact seems to have been buried. Clinton won in 1992 with 43% of the vote because H. Ross Perot had an axe to grind with George HW Bush and made it his mission to deny re-election. (Also, HW failed 'purity' tests himself.)

And Biden beat Trump because Trump was an objectively terrible President. But, in spite of that, and because the Democrats didn't thoroughly bury him when they should have, he resurrected and beat another milquetoast centrist.

You cannot seriously argue that leftists cannot win general elections when a) they are never allowed to be the nominee and b) the center refuses to respect primary results when they lose, siding with Republicans to defeat leftist Dems (See, Ned Lamont, Zohran Mamdani.)

Of course leftists can win elections (and do in my country). Let's do maths and stuff! Imagine a bell curve of voters. You and I stand on the left of the curve. Way out on the right is the GOP. We want to pick a candidate to win the general. Are they from where we are? The centre? Somewhere else?