Admittedly, few people would think to check ahead of time, but it is noted in the World of Hyatt Terms and Conditions:
“
Ineligible Rates” are all rates other than Eligible Rates and include Free Night Awards (as defined in Appendix B), complimentary nights awarded in connection with Miraval’s Authentic Circle program, rooms booked on third-party online retailers (such as Expedia.com, Travelocity.com, Hotels.com, Booking.com, Priceline.com, Tripadvisor.com, Inspirato.com, home-sharing sites, or any other third-party online/mobile travel portal or bookings made directly on Google.com and TripAdvisor Instant Book), traditional wholesale rates (examples include, without limitation, GOGO Worldwide Vacations, Pleasant Holidays, Tourico, and Hotelbeds), airline crew rates, airline employee rates, travel agency employee rates, media rates, Club at the Hyatt discount stays, Hyatt employee or employee family or friends-and-family discount rates, airline interrupted-trip vouchers, or contracted rooms.
Source:
https://help.hyatt.com/en/hyatt-term...att-terms.html
The reasoning behind this restriction relates to commissions. Websites like Expedia and Travelocity make money though commission paid by hotels. But, hotels also have to pay for points. Hotels (many of which are franchises) aren't keen to pay both a commission and a fee to give you points.
As
mahasamatman notes, most (all?) major hotel chains now incentivize guests to book direct with the chain by only awarding frequent points to people who book direct.