The real challenge is 25 1-night stays without repeating a single Hyatt!
Might get you one of the special gifts for staying in 25/50/75/100 different Hyatt hotels...
In all seriousness, one of the advantages of switching hotels each night is to get the 1000 point diamond amenity for each "stay". So although potentially more of a PITA, you do get rewarded for it.
However, like others have mentioned, I wouldn't really want to explain to corporate why I felt it necessary on a long business trip to switch hotels every night in the same city for personal reasons rather than staying in the same place and being more relaxed / productive.