AAA or not, Crazy Taxi was an arcade game so we can only hope they don't veer the taxi off a cliff, or do veer it off a cliff (pun intended) as is appropriate for a good Crazy Taxi game!
Deus Ex, Doom, Mortal Kombat, Mario, Need For Speed, Sonic The Hedgehog, Tomb Raider etc. all have had AAA reboots and not always following the same formula as the originals. AAA games tend to chase the latest trends, reboots included. This isn't to say all AAA reboots fail.
True about Deus Ex. But then the original was very much an early 2000s PC shooter (which do not work on consoles) and Invisible War was a disappointment.
Mortal Kombat
The first reboot didn't change the gameplay all that much. It was more of a story-necessity to do a reboot: Armageddon ended with all the fighters dead. Ditto with MK11 but MK1 did change up the gameplay a bit more.
Mario
Mario? Mario as a franchise never really has been rebooted. Certain genres of Mario have though, like New Super Mario Brothers on DS.
Sonic
Oh boy...are you talking about 06 or Boom? Actually it doesn't matter... Both are examples of how not to reboot a franchise.
Tomb Raider
The tomb raider reboots (both of them) do kinda make sense as all three eras are completely different gameplay styles.
Can't comment on NFS, never really paid attention to the franchise.