There is a real reason that the caps are painted. Glass beverage bottles are usually stored in a crate and grabbed from the top, so the design on the lid is what restaurant or store employees used to distinguish what drink is contained within it. This allows employees to distinguish similar-coloured drinks (e.g. Coca-Cola vs Pepsi or two different brands of beer) just from looking down at the top of the bottle.
But there probably is a way to paint them without using plastics