It's not that languages develop a word for blue last, but that there's usually a specific order in which terms for colour enter languages. It's roughly as follows: all languages have words for white/black, if they have 3 terms for colour the third will always be red. After that it's green and/or yellow. Only then do you get blue or blue-and-green. This can also be seen in the writings of Homer where honey is described as green, and hair is described as... blue, that is, the same term was used to describe the sea as well as corn flours (i.e., a dark colour). It's with Empidocles that we see the classification of colour the Ancient Greeks would have used: light, dark, red, and yellow.
After blue/blue-and-green the order breaks down a bit, but new colour terms obviously come into use after blue. In English for instance the terms for pink, orange, and brown all came long after blue. Coincidentally brown is usually one of the last colours to get its own term, and in English before the term brown was used to refer to a colour it referred to dark or dusk.
What might be missed is that black and blue are not necessarily differentiated. I know that, at least among Indian languages specifically Sanskrit, black and blue aren't as differentiated as they are today. A dark color/black was seen as dark blue.
I would imagine the dyes were referred to by the materials used to create them, cochineal for a red dye, woad for a blue/indigo dye, etc. The etymology of purple does come from a shellfish or a fish and purple dye did historically come from a sea snail but the name for that particular dye likely didn't come from the same root as purple.
Pink and orange are not basic color words. They're the names of physical objects co-opted as a general color. It's the same for all the cultures that don't have a word for blue. Their users just refer to blue as the "color of the sky" or the "color of bird X". Same as English using the "color of this citrus".
After blue/blue-and-green the order breaks down a bit, but new colour terms obviously come into use after blue. In English for instance the terms for pink, orange, and brown all came long after blue. Coincidentally brown is usually one of the last colours to get its own term, and in English before the term brown was used to refer to a colour it referred to dark or dusk.