>the places with the strictest border controls are often those that are quite desirable
cheeky counterexample: North Korea
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North Korean border control is there to stop people from leaving, not entering.
Uhm, no: if you try to cross the border in they will shoot you just the same.
I presume it's also to keep out subversive foreign agents. And reporters. And people whose mere presence is suggestive of Western capitalism and therefore subversive. Something like that.
i.e. basically everyone
Pay a bit of money in China and you'll have a visa in no time. That's doesn't work with, say, Switzerland, at least not with a similar amount of money.
Most countries (including Switzerland) have some form of investor's visa which is basically an official way to pay for a visa.
Which is a very different thing and will set you back ~1m, not a few hundred.
Visas are still for sale, they're just more expensive (like so many things) in the US and Europe.
My aunt was forced to leave China as her husband's work there (for some multinational) was done. Instead, she started her own business (not for the money, but to have a presence which 'stimulates the local economy'). Now she's allowed to stay in China.