Here is a data point that could be useful.

In 2024, I booked all my IC stays directly with IHG through cashback sites, or through travel agencies (the ihg luxury and lifestyle program which gives EQNs and EQPs). I earned 220k EQPs (all from IC stays) at the beginning of December 2024, 40k of them are stays booked from travel agencies, and did not receive an invitation. Then I gave up the travel agencies and booked all my stays directly with IHG (still through cashback sites), earned another 70k EQPs in Dec, and finally received an invitation.