With enough pressure I could see a reusable-dishes-as-a-service type company. A restaurant could pay this service $x per month and the service would come daily to drop off clean containers and pick up used containers for cleaning and sterilization. Restaurants could have a deposit upon getting a meal, say $3. When you bring your containers back you get your $3 back (or $3 towards your next meal there?).
If multiple restaurants in your area used the same service, or if the dishes were standardized enough, then you could drop off your used dishes at multiple different places whenever you get take-out again.
Obviously this is "in an ideal world" thinking, but it seems like with enough economic pressure on the take-out industry it could start being feasible.
The earlier comment was about people bringing their own silverware, dishes, and cups, with a washing station at the restaurant.
I think you've switched it to takeaway containers for take-out? That's a rather different topic. Certainly we know that recycled glass containers worked for decades.
But the main issue is non-biodegradable objects. Why would we worry about returnable-reusable boxes to replace, say, cardboard pizza boxes?
If multiple restaurants in your area used the same service, or if the dishes were standardized enough, then you could drop off your used dishes at multiple different places whenever you get take-out again.
Obviously this is "in an ideal world" thinking, but it seems like with enough economic pressure on the take-out industry it could start being feasible.