More processing capacity for your application (no need to share with OS), no more interruptions by the OS that are unpredictable in duration, no more interruptions by the OS that are unpredictable in terms of timing and priority and above all, since this seems to be the main goal of the software we're talking about: lower overall latency. Standard C++/JAVA (as far as I know) talks to hardware through a software layer (the OS's system calls). This takes time. Time you can save by cutting out the middle man.
There are apparently ways to do this with an OS running in parallel as well though when you have multiple cores available apparently (see another comment to this thread).
You can get all this by pinning to a core and DMA to hardware. Think of the OS like a library - if you don't call it and don't ask it to call you it stays out of the way. There's no need to throw away the OS.
This is exactly what is done. OS’s are really nice to have around and will stay out of the way. In the day and age of fpgas no reason to ruin the software side to maybe kind of sort of get a bit faster in your software?
There are apparently ways to do this with an OS running in parallel as well though when you have multiple cores available apparently (see another comment to this thread).