Yes, which is why only empty drink cups are allowed in the bins. If I recall correctly, they added bottle holders to the outside of the bins.
I stand out as an American at Canada's Wonderland, as nearly all the locals have draw string bags, containing everything but the kitchen sink. (Having zippered pockets, I have never used the bins.)
Canada's Wonderland definitely considers the bin system a success, as they added it to Wonder's Mountain Guardian. For years, the number one guest complaint was being forced to buy a locker to store bags for WMG.
I wonder at Cedar Point, if I show up to the entrance of TT2, and have no credit card or cash, but have a car key, will I not be allowed to ride? Maybe the park can add a couple thousand free small pocket item lockers outside the ride like Universal does? I am personally excited to have a line with no cell phones. As the squeal at Moreys Pier says, you can pass the time talking with other people - or twittling your thumbs.