The boot up time is the main benefit. The other benefits, anything the OS runs will also be SSD fast which you want, because by nature windows is multitasking while you run your game or other ssd application any latency caused by background processes will cause less impact.
Let's say, you have a usb device that starts to fail and create logs. If the OS is on HDD then the system log will also be on HDD, many errors will start to introduce lag because it's on HDD. If OS is on SSD, will less likely to cause an impact.
Other reason, very few games will benefit from SSD like Fallout / Skyrim. Makes no sense not to have OS not on SSD, since it's running the application you want to be fast. Both should be fast, PC is not a console. OS on SSD, some games also on SSD, the rest on HDD. Simple!