Can I clarify my understanding of a few points? Kelly can correct me if I'm wrong.
Epson desktop printers (not sure about the pro ones) generally do at least a "mini-clean" each time they're turned on. The amount of ink that is discharged is minuscule, but you'll still hear a lot of noise, which is mostly just the pump working to drain whatever happens to be contained in the capping station. Is that correct? Some people leave their printers on to avoid these mini-cleans.
Epson desktop printers have an algorithm which determines how often it needs to do a regular head clean. I've never really understood how this is programmed. If you leave your printer off for a week or more and then turn it on you're highly likely to trigger this. But you won't avoid it by leaving the printer on, and even with regular, heavy printing you'll find that head cleans are triggered at moderately regular intervals. The printer seems determined to push ink down the waste tube. But if you turn the printer on regularly then you shouldn't get a full head clean on every such occasion.
I don't know how Larry was managing to put a few drops of flush on the capping station (don't have a 3000), but if it involves unplugging the printer and moving the head, then on my printers at least that will almost always trigger a head clean when turned back on.
You also shouldn't fill the capping station with flush and then turn the printer off, leaving the capping station full or mostly full. If that moisture comes into contact with the print head, it can provide a conduit to the ink in the carts and start a capillary action that will wick the ink out of the carts and drain them. An expensive lesson.