Tooth loss associated with increased cognitive impairment, dementia

This is correlation, but it is very unlikely to be causation.

Having a bad health will certainly cause a person to have all kinds of problems. For example, if your food does not contain enough vitamin C, you are likely to get some form of scurvy[0], which might lead to loss of your teeth, but it will also lead to a lot of other problems.

[0] https://en.wikipedia.org/wiki/Scurvy

> In addition, tooth loss may reflect life-long socioeconomic disadvantages that are also risk factors for cognitive decline.

This is not "in addition." This is another "poverty found to be associated with poverty" study.