Joe Biden has the same approach. Biden was arguably the most moderate of the nearly 30 Democrats who ran for president in the past year. The team around him, the folks who would presumably lead his administration, are Clinton/Obama veterans and not exactly a bunch of left-wing woke activists: Mike Donilon, Ron Klain, Anita Dunn, Jake Sullivan, Jeff Zients and Bruce Reed, one of the leaders of the moderate Democratic Leadership Council.
They understand they are leading an extremely broad coalition and have done an excellent, underappreciated job of incorporating both moderate ideas and ideas from the Bernie Bros.
To the extent that Biden’s gone “left,” it’s mostly in areas where the moderates agree: quadrupling federal spending on low-income housing assistance, making community college free.
A Biden administration would not be further left than the Democratic voters out in the country or their representatives in Congress. Those voters are not mostly the urban gentrifiers who propel the left; they are mostly the “somewhat liberal” suburbanites and Black moderates who gave Biden the nomination.