Actually, you don't have to have it running all the time. You need to let it run on startup, then you can just right-click on the small icon in the system tray, then select 'Exit Eraser'. It will still run when you start it from the desktop icon, the start menu or a context menu.
Eraser 6 is different from Eraser 5, in that not just the scheduler but also the erasing engine run in the background process, but, if the process is not running, it will start when you run Eraser. Eventually, the background process will be replaced by a service, that is will run even further in the background. Eraser is designed in this way to overcome the difficulties created by the changes to the security model in Vista and now Windows 7. My own view is that, as the background process does not appear to affect performance drain system resources, even on my old and slow XP laptop, it isn't that much of an issue. I do disable as many startup programs as I can, but I let Eraser load as I use it pretty much daily.
The next version of Eraser will have the option not to start Eraser with Windows, and thus of course to lose the scheduling function. I used to share your doubts about the usefulness of scheduling an erase, but now I have Eraser clear the contents of the Recycle Bin each day, which is for me a useful piece of automation.
David