FIFA doesn't insist on building new stadiums so much as they award bids to countries that don't already have sufficient stadium capacity. Brazil and Qatar need/needed to construct stadiums, and so does Russia probably, but had they accepted the England and USA bids for 2018 and 2022, respectively, no stadium construction would have been required (at most, perhaps some renovation). In fact, either country could host a World Cup with only a few months' notice.

If you want to siphon cash, you must be near a flow.