For an official government web site, FAQs have an additional downside - some people will (perhaps maliciously) regard the FAQ answers as the law. Or as official policy. Or similar stunts. This can get you into having lawyers regularly review the FAQs, answers that are half disclaimers, and other messes.

That said, there are many cases where I find FAQs useful. Especially for learning the basic (and oft undocumented) assumptions behind something. Or as a TL;DR alternative to marketing blather, clueless salespeople, and mediocre documentation.