> Wouldn't they rather be arbitrarily rich instead?

Generally no, though you won't get this answer directly.

Many people prefer to be rich relative to others than arbitrarily rich. If you ask a bunch of random folks if they'd rather be in the middle class in their current country of residence in 2005, or of noble birth in ~1100 CE, you'll get the latter answer _a lot_ despite that being an objectively worse quality of living.