A proof of concept optimises for one thing: showing the model can do the task at all. Production optimises for something else entirely, which is that it keeps doing the task, correctly, under load, for people who did not build it.
In our experience the blockers are rarely modelling problems. They are evaluation harnesses that were never built, data contracts that were assumed rather than agreed, and no named owner for the system once the pilot team moves on.
The teams that ship start from the operational end rather than the demo. Three things tend to be settled before the first prompt is written: