FILO is useful because it allows for data within the stack to be restructured before it is accessed. Specifically, FILO allows things to be reliably reversed. If you have a situation where inner elements are returned before outer elements (as might be common with recursion) then the FILO is perfect.
http://www.i-programmer.info/babbages-bag/263-stacks.html?start=2 Has an excellent explanation of the utility of the FILO paradigm.
As for interrupts, again the utility is that subroutines will call an interrupt before anything else.
There are actually a few reasons that FILO can be useful for interrupts. http://www.eee.metu.edu.tr/~cb/e447/Chapter%204%20-%20v2.0.pdf has an introduction to the concepts. One example would be when it is desirable for registers to be pulled from a program and restored to a program in reverse order.
This article has an animation that demonstrates the exact utility of FILO: http://users.ece.utexas.edu/~valvano/assmbly/stack.htm