EDITING POST, as I tried after signing in to see if that made a difference and it did not.
The issue does not seem to matter if I try for 2 Adults or 2 Adults and 1 Child.

I am just exploring Hyatt as a possible option to transfer Chase points to and even possibly signing up for their branded CC to obtain points.
I am a member from a few years back but have no recent experience with the brand.

Have been using Hilton and their points so can only compare that as reference.

When I search for bookings on Hyatt.com when I search by points it shows me available options for my party and dates.
2 Adults / 1 Child. Sept Dates / 2 nights
Looking at options in both Paris and Barcelona.
Multiple options come up as point options on the left hand site, but then when I click check rates
It opens me to the booking window and states:
"Unfortunately, this hotel is not accepting World of Hyatt points or award during those dates. Explore our other rates or modify your search."

This was true for 6 of the 7 hotels I looked at that were stating available for X points on the left side.
Yet, they each show an available standard rate and a member rate ; are those not standard rooms that should be bookable on points???

why does the initial search not recognize this and not show these as point options???