If you don't want to risk detergent residue, you can still backflush with water, and I would do so on a daily basis. I was just helping a friend with a Classic just purchased from Craigslist, and a few rounds of plain-water flushing got the (initially completely blocked) solenoid back in functional shape.
BTW, Amazon has "Espresso Supply 902070 58mm Backflush Insert, Set of 3" for $11.50. (Eligible for free shipping or Prime, too.) Great deal there, at least if you want to keep more than one around.



