It would be wise for you not to stereotype Western teachers in China or elsewhere. Desperate old pensioners? In most provinces nobody can work after they are 60 years old. It rules out most of the "needy pensioners" you spoke about.

Most older men in China don't work, although there are still quite a few guys 55 to 63 years old who are teaching legally.
FYI, many older FT's in China are financially secure, and only teach for the work visa ( mostly at universities ) if they are not married. I have known plenty of FT's who had money. Teaching in China is low pay, so obviously nobody would teach in China for the money.

As for women, sure, maybe some can get something back home, many can't, you should know however that is a type of cultural difference. In the West most younger women are not interested in men thirty years older than themselves. Now is that the man's fault? No, it's just how it is. You could be fifty-five years old in Australia or the UK, be slim, fit, handsome, you ain't gonna snag a 25 y/o woman, no way, unless you are extremely wealthy.

Asia, including China is different. Even average non-rich men in their mid forties or early fifties can snag women in their mid to late twenties.

A 45 or 50 year old man is "old" in the West. In Asia he is mature fruit, ripe for the picking.

Your post is really stupid, you should know better!