Since the Freestyle machines were broken (and then removed completely half way into the cruise), there was no need to have the plastic cup at any time on my sailing. Instead I just showed my "Coke" sticker on my room key and was given soda at the bars. I did sometimes use my Coke cup, but often the bartenders wouldn't serve the drink in the plastic cup (probably because of germs) and instead would pour it in a fresh glass and have me pour it into the plastic Coke cup if I wanted to do so.
I agree, if there were Freestyle machines all over the ship (or at least Lido and Promenade decks), it would be much better (and I would have carried around my cup). I'm guessing you are right, there is probably a chip in the bottom of the cup. I've seen much smaller Freestyle machines now so they could place them around the ship without it being an eyesore.