I'm referring to the HEROES Act. The next proposed stimulus bill that was supposedly put together almost entirely by Pelosi and her staff. I know Democrats don't currently have the power to pass whatever they want. But they do have control over what they personally write and propose. Pelosi is in a prominent and powerful position, and consistently uses it to initiate negotiations with pathetic lowballs that ensure the actual final outcome will be terrible and otherwise actively prevent good things.
Ah yeah, I forgot that HEROES has another $1200 in it. (They did amend the lobbying firm bit at the Rules committee, albeit imperfectly.)
HEROES does have some further provisions for 'the average person' - there's the 'premium pay' provisions for essential workers, the tax section has a bunch of EITC stuff that I admittedly don't have much expertise on, medicaid provisions, an extension of unemployment benefits for another ~6 months, and other bits and pieces.
(In my opinion the whole 'premium pay' thing is something of a sad farce. Hazard pay of $13/hour minimum wage, with a cap on total earnings at that rate?)
And it wasn't just a Pelosi package - committee leadership were involved in various portions of it. (Of course, most of the committee leadership does not err leftward on the political scale.)
As to your point of what they write and propose, the theory is that if they go 'too far left' their proposal gets laughed off by the Senate & WH and becomes a waste of effort. See: much of the House counterpart to CARES, which was casually dismissed and ignored. (Also see: 99.9% of what House Republicans did during the Obama administration.) Heck, HEROES is already getting ignored by the Senate, at least for the next few weeks, because McConnell almost-literally wants to see people suffer more before moving to the next round of aid.
Oil owns the D, too.
Obama was pretty bad in his first term on oil (and other environmental topics), yeah, but did get better later on. I assume he was viewing things through a cynical 2012 reelection campaign lens.