My, my. Sounds like you all are giving up on traveling "through the back door" (seriously, no pun intended, those are Rick's words) and refusing to "live like a local".
Seriously, this is not a ruse that the Greeks are foisting on gullible tourists, this is how people live every day, in Greece, and many other countries I have been in. To think that anyone else involved in the process even bats an eye (except for the large amounts of toilet paper Americans seem to use) is no concern, it is completely your own discomfort; a good opportunity to "broaden your horizons through travel". Oh, have you heard about the squat toilets, better known as the hole in the floor?
If you really have discomfort over someone else disposing of your waste, then at the least take the bag out and tie it or seal it before housekeeping gets there for the day, maybe dispose of it your self. Taking the smaller bags might be OK, but keep in mind you are just increasing plastic waste, you accomplish the same by tying the bag once a day yourself.