Actually, you CAN teach a dog to put the toys away. Sacha used to do it reliably...she's not allowed toys anymore...so I'm not sure if she'd still do it, but she'd probably re-learn it fairly quickly.
Sacha is INCREDIBLY food motivated...so I did it using food (though you'd probably be able to use clicker for it). First step is giving all the toys a name....Sacha had lambie, football, monkey, rib-it (a frog), moo-man (cow), etc. When it was time to clean up, I would tell her to "get lambie," then have her "bring" it to me. I would be standing next to the toy box. When she "brought" it to me, I'd hold a treat OVER the toy box, when she dropped the toy, I said "Yes, good clean up." Because I held the food over the box, she'd drop the toy IN the box to get the food.
Eventually she learned that "clean up" meant to drop her toys over the toy box. At first I had to tell her to "clean up" individual toys ("clean up lambie"), but eventually she figured out that "clean up" means all her toys being put back!!!!
To KEEP my house clear of toys, I just used the "bring" command ("bring lambie") - she learned that she was only allowed to play with toys if I told her to "bring". She'd get that out of the box, and that would be her toy.