@Danger. You took the first step by recognising that a precision thread is not needed.
If we did not challenge ourselves with new problems we would never learn. Having to answer another's questions forces us to crystallise our understanding.
After encountering three different plastic thread problems last week, I can now summarise my experience in just two paragraphs.
1. The tensile strength of an injection moulded cap was insufficient, so it tended to split over time. The manufacturer used progressively cheaper material. It was doomed to fail in the end because material quality was never defined or tested. Design of the seal so as to not require high tension in the cap material would allows a cheaper plastic to be used. Tension in the cap must be opposed by compression in the neck of the bottle, so a better seal design leads to savings in the bottle also.Thread profile can magnify tension in the cap. Too fine a thread can also lead to high cap tension.
2. Solve a sealing problem with an unusual large diameter screw cap. It came down to final dimensions and how the product was trimmed after moulding. Different materials for cap and bottle lead to thermal size variation, that requires larger sealing cones and relatively bigger threads.
3. Find an alternative cap for an existing bottle. This got me to wonder what standards there are for plastic bottles and their caps. I googled 'plastic bottle thread standards' for enlightenment.
Since the cap is fundamentally used to provide a seal, the seal should be designed first to meet the requirements specified. Next, the screw thread requirements can be considered. Final material specification follows. All of those must have the cost of manufacture in mind. The container is there to protect a more valuable product. The quality of the product is finally dependent on maintaining the quality of the packaging.