I somewhat agree, but depends on the player.
Like if the player consistently dropping passes or suffering breakdowns in coverage isn't a Lamar Jackson-level player, then they'll replace the player first. Like if the decision is between cutting (or in this case, not re-signing) Peters or moving on from MacDonald, they'll choose to keep MacDonald in a heartbeat, as well they should. There's only a handful of players on any team that the team is actually married to, and pretty much only the QB or some super rare all-time great, like a Ray Lewis, is going to win a power struggle with a coach. Everybody else, largely, is replaceable, and most franchises will look to make personnel changes much quicker than coaching one's.
As for coaches/FO, in many organizations, they're largely tied to each other. Its not a certainty, but in many cases, they're linked. Meaning when the HC goes, the GM usually is either gone too or soon to be gone. Firing assistant coaches or even coordinators can often be considered the "easy choice", though there also aren't a large number of examples of those firings turning into great things long term. They're mostly just scapegoating certain positional group coaches or play callers for larger issues within the organization.
I totally disagree with the last paragraph. In some cases that'll work, but in the NFL in particular, I think history would tell you that a TON of franchises go through a TON of GMs, HC's, coordinators, etc. over time, and none of the new guys make a material impact on the organization's ability to win games, transform culture, etc. I'm sympathetic towards a change being needed in some cases, but there's a reason why there's such a huge amount of turnover among HC, GM, etc. on an annual basis, and wise there's just such a huge quantity of organizations that perpetually fail over and over and over again.
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