The problem you'll see moving forward if Biden goes hard left (which thankfully he won't) is that he won't have the "anyone but Trump" factor influencing the turnout.
That's the reason the "left" did well here - the more left you are, the more enthused you were to go out and vote against Trump. But what happens when Trump isn't a factor?
Basically nobody voted for Biden. Hence the wild celebrations when he won that were basically all about laughing directly at Trump.
This doesn't make any sense. You are confusing your terms, and really don't grasp the basics of American politics.
In the United States, the left is far less prone to hysterical shrieking over Trump, whom they regard as as much more consistent with American tradition. The left in the United States is motivated primarily by policy - health care, student debt, climate change, drug policy, minimum wage increases etc. - such that one of the major themes in media coverage for the past two years has been whether the left would actually turn out for a 'moderate' like Biden.
The people you are thinking of are liberal Democrat centrists, who are mostly indifferent to economic issues but who care profoundly about identity politics and who have flooded the internet for the past four years with ill-conceived gibberish about fascism and Putin -
most of which later turned out to be false.
These are the people who were motivated primarily to vote for 'anyone but Trump'. They are the ones who can not be counted on now that Trump is gone.
We will have a clearer picture when the follow-up surveys come out, which are always much better than the exit polls, but it is already clear that the appeal to moderate 'anyone but Trump' voters was not what won it for Biden. Trump actually increased his share of the vote among Republicans, while eating away at the Democrats' core of minority voters. Along the Texas border (at least 80% Hispanic), some counties swung more than thirty points for Trump. He also slightly increased his share among African-American voters, which, as anyone who follows American politics knows, is beyond catastrophic for the Democrats. In 2016, even slight dips in African-American turnout (never mind switching parties) probably cost Clinton as much as anything else.
Hysterical anti-Trump twitter liberals did vote in large numbers for Biden - but they mostly live in states which have not voted Republican since the Civil Rights Act, and which in the American system are essentially irrelevant. What swung the election in the states that mattered - Michigan, Pennsylvania, Wisconsin, Georgia - was years of dedicated grassroots organisation to get out the vote by the very progressive groups that the Party elite loathes and is now trying to blame for its own mediocre performance.
And as if that wasn't enough, the Party is also preparing to swing to the right, which will not only further alienate its own base but also Republican rank and file voters, who support left wing economic policies like Medicare for All, climate change action, drug reform or minimum wage increases by significant majorities - which is why, for example, the $15/hour minimum wage proposition passed in Republican Florida with nearly 15% more support than Joe Biden managed.