This is just half of what Time Machine does. What people are constantly missing is that Apple Time Machine is
fast, as it does not need to walk through the whole filesystem to find changed files. Thanks to FSEvents, introduced in Mac OS X Leopard, it knows which directories actually contain changed files and hence usually only needs to check a small fraction of the filesystem. (Not sure if it still works that way after the switch to APFS).
This would of course also be possible on Linux (using *notify), and there are some projects which try to do this, but it's really hard to do it reliably. You might argue that this feature is less important nowadays because NVME SSDs are so fast, but still, I remember very well how astonished I was that creating a new time machine snapshot on OS X Leopard took mere seconds.