I don't disagree with your description of events, but you're imposing a reasoning behind them for which there is little evidence. The idea I'm pushing back against is that vaccines (here Covid) and I suppose now Covid policy in general, resulted from some clever metric of keeping people alive because of their income generating value. There's no evidence government works like that, and masses of evidence that government decisions are in fact a mix of submission to industry lobbying, blatant electioneering, and simple incompetence.
Whatever the policies were, they would almost certainly have been whatever the loudest industry lobby, focus group committee, or egotistical politician wanted at the time. Not some sociopathic genius doing life-value calculus.
Health insurance costs in America have risen by over 130%, so there's no evidence of insurance companies offering flu shots to save money, they just demand more premium to cover it.
Far more likely, in my view, is that taking regular vaccines has become a marketable product (for various reasons) which insurance companies have jumped on. Offer the shot, up the premium to cover it (plus a healthy profit). It simple market expansion.
If there's a market (or one can be fabricated), then there's a product to sell. If you can add a flu shot, up the premium to cover it, and not lose customers, then it makes sense to do so. Doesn't have any bearing on whether it works. Same metric would apply to a medicine which did absolutely nothing whatsoever. As long as advertising it justified a rise in premiums larger than the cost of it, and customers don't jump ship.