I think the main benefit is the safety aspect. For example, i'm doing a rehabilitation program for an injured shoulder and I do quite a lot of BB and DB floor pressing and will gradually progress to full range of motion bench press.
It's also used to increase strength from the mid point of a traditional bench press if this part of the ROM is a weakness. Same concept as the 'Board Press'.
Here's a good description of it,
Also, it's not quite like a bench press with your feet up as it's normally done with an arched back and bench pressing with your feet up will flatten/straighten your spine. That's mentioned in the link anyway...
Even when I am able to bench again, which i am very close to, I will do floor press every so often just to give my shoulders a break... Which is worth a thought 'down the line' in your training..