Bad teeth also harbor bacteria that have been shown to exacerbate cardiovascular disease, at the very least. Not saying this article is claiming that as a casual mechanism, but diseased teeth are known to cause other systems to also become diseased.

There's a known causal relationship between mouth bacteria and heart disease. It's thought that mouth bacteria cause systemic inflammation, which leads to the damage that causes heart disease.

We'll likely find it also contributes to Alzheimer's (as, it seems, all pathogens and pollutants in the body seem to do).

Mostly, yes. Also genetics, what bacteria happen to colonize your mouth and what types of food you ate while your jaw was developing. That changes nothing about the article though, that dental hygiene can be used to predict mortality and aged care demands.

The correlation is the other way around, in my mind:

those that fall to acute infection, or indeed gut/systemic infection, will show poor oral hygiene,

and both are implicated in diseases that shorten life expectancy.

Idk, my cat's vet measures the cats age based on the plaque on their teeth. Pretty sure my cat's not wealthy and has a tendency to over-eat.