I sort of wish Obama had more influence. He tried to tell Biden not to run in 2020, which definately would've been a better outcome even if the Dems coalesced around a different centrist.
He asked Biden not to run in 2016, and he didn't, then urged donors to support Hilary over Bernie. In 2020 he asked other candidates to drop out so Biden could run, and they did. I'd argue he has that influence you're longing for and it hasn't been that positive.
Yeah, they were never going to let that happen. They'd preferred Trump over Bernie. Would've been hilarious to see Chris Matthews freak out even more about Bernie death squads rounding people up and executing them though.
The problem WAS that people preferred Bernie, same as every other populist candidate. The last ones that won resulted in a Term limit and an assassination respectively.