SD cards: stuck with FAT16?

This page says that SD cards must be formatted as FAT16 and that the 8.3 filename scheme must be followed. However, I wonder if there is some library that will allow me to use some other filesystem (UDF, for instance) without that old DOS limitation, or if such a thing is even feasible on an arduino.

I use UNOs, Nanos and other 8-bit boards. Would any filesystem other than FAT require too much processing power? Or is there a particular reason for FAT to be apparently the only option?

I have not read that page before.
This is the SD library reference:
Here is a note about formatting:

You can use FAT32, but not the addition of longer file names.
As far as I understand the SD library already uses a large amount of RAM. Allowing longer file names would require even more memory, and there will be no runtime advantage.

There are a number of SD libraries with long file names, some are no longer maintained, others are questionable.
There is one exception: The original author of the Arduino SD library is Bill Greiman. He has improved the SD library and supports now long file names. I don't know if that will fit on a Uno, but you can try:
Perhaps the long file names are automatically turned off for a Arduino Uno, I'm not sure, I did not read everything.