Okay so I know that I just poo-pooed this story as having no details and basically being an article written exclusively based on a conversation with "A former Republican house member who is close to the Biden transition"..... And that we shouldn't even waste mental energy thinking about this for at least another three weeks.....
BUT EVEN I CAN'T HELP IT
Charlie Baker is explicitly mentioned in the article. It seems unlikely because Baker has not endorsed Biden and it doesn't seem like he will, but rather Baker will go into the election quiet and then say that he wrote in his grandmother or something. I don't think that Baker would get an offer unless he specifically endorsed Biden in the campaign, and the clock is ticking, Massachusetts just started voting on Saturday.
BUT because Baker is explicitly mentioned in the article, I think he'd be a good addition as a HHS member, but more importantly, politically, it'd also open up the 2022 Massachusetts gubernatorial race for a Democrat, as Baker is very popular, Karyn Polito his Lt. Governor is not as popular, and there are no high profile moderate GOP gubernatorial candidates in Massachusetts: Geoffry Diehl [who unsuccessfully challenged Warren in 2018] wouldn't stand a chance, the guy trying to challenge Markey is going to lose badly and is a nobody, and this is a rough year for the GOP in Massachusetts so finding a successful candidate in 2 years is going to be challenging. Democrat Maura Healey, the Attorney General, would be a top candidate to run for Governor, and she's been very popular, she'd likely win against a really weak GOP. As is today, Healey is unlikely to challenge Baker. They've worked closely together and while Healey criticizes the Baker admin from time to time, the concentric circles of their support are almost the same... The people supporting Healey also generally support Baker, and vice versa (Baker polls better with Democrats in the state than Republicans). If Baker were running in 2022 (unknown at this point, although he has no place in a national GOP and he knows that; MA governor is the highest office he'll hold in Republican politics), I suspect Healey would run again as A.G., they'd both win. Appointing Baker to a technocratic position in HHS (Baker was previously the CEO of Harvard-Pilgrim, and then was on the Board of Beth Israel Deaconess) would open up the 2022 MA Gubernatorial race for a Democrat.