Update from Recent Wish sailing 7/19-22:
Requested private table.
Went to Triton's at 12:30 on embarkation day to check on the reservation to see if we had a private table. We did not. Again

We have never been given a private table when requested, but every other time on the Dream and Fantasy they switched us then to a private table. This time they said the ship was full and no changes could be made, but to refresh your app at 4:30 to see if we got a new table. For more information- we are a table of 2, late sitting, and were first in line requesting changes to late seating private table. There were two other groups in front of us at Triton's requesting private table for early seating and were told the same thing as us.
4:30 came and went, no changes to our table. Lots of people missed this cruise do to the first day being Friday the day of the Crowdstrike computer problems and flights being canceled (were told from staff between 10-20% of guests couldn't make the cruise).
Went to dinner at Marvel at 8:15 and at the entrance asked again about a private table and they found one for us

Yaa. So all hope is not lost if you don't get a private table right away or even after asking the first time. Try try again.