Once again, a seat at the table means influence *inside* the administration.
The progressives who believe in this strategy - Bernie, AOC, etc in the legislature, and think-tanks like DFP - fully endorsed Biden, touted him to their followers as a chance to have the most progressive presidency ever, raised money for him and the party, and did this all before winning any personnel or policy concessions. They have not just shown compromise, they have shown that most storied political gift - pragmatism. They showed this pragmatism again when, as you pointed out, Bernie and Biden had a task force to come up with joint policies. You take that task-force seriously, and these progressives do too, and it showed very directly that they can compromise on climate policy. There are many piecemeal healthcare policies, like drug importation and a public option, which these progressives are happy to support without having an enitre M4A along with it. For example, Bernie is the sponsor of a drug importation bill in the senate which is totally divorced from M4A legislation. Flexibility, and the ability to find common ground! And yet, Biden will not appoint these pragmatic progressives, that worked for his campaign to his cabinet.
Perhaps this was right?