It's not technology; it's attitude.
FAT came about when Billy designed the DIsk Extended BASIC for the Altair 8800 (on 8-inch, single-sided, single-density floppies, capacity 256kb). It was simple and compact enough for such small volumes, not to mention drivers simple and small enough to share elbow room with the rest of the system in a box with 16Kb of RAM. (Yes, hard to believe it. The 8080A and Z-80 had 16-bit memory addressing, hence a maximum of 64Kb of RAM accessible directly, but memory was expensive and lots of systems ran with 16K.)
I'm not sure what kind of filesystem CP/M-80 had, but when Microsoft edged out Digital Research for the contract to provide operating systems for the new IBM PC (sad story about Gary Kildall there), FAT came along with it. Quarters were still cramped. The 8086/8088 could address more RAM but still not a lot (640K I believe, hence Billy's embarrassing quote that nothing would ever need more than that), and double-sided double-density 5-1/4" floppies held somewhat less than a standard floppy does now.
So, FAT made sense then, but it's a living fossil now.
So, why not, as said here by many, scrap it for something better?
Look at Linux and NTFS. M$ has stubbornly refused to disclose even the minumum information about that filesystem needed to design a third-party driver for it. Why? It's not the kind of technology that others would seize upon and exploit competitively. It seems to me that they want to frustrate any attempt to access their media with anything not their own.
Sure, drivers for other OSes can be had, but that's only useful for user-created volume (granted, the most common case). Microsoft is not likely to start supporting any non-M$ filesystems and wherever they control the design of things, if history repeats, they will go out of their way to avoid using anything they can't control.
There are people who are pathological control freaks. The same can be true of corporations.