Why are resistors used in LED strips?
Your question is not to difficult to answer.


By connecting each led to its own resistor it becomes very simple to cut the strip to length without losing a whole section of led due to a wrong cut.
During the production process the two carriers can be connected with led resistor combinations. That makes the production process very simple. 
When a led fails you only loose one led in stead of a whole chain


There are strips with leds in series with marked cutting positions but mainly the leds are put in parallel over the supply line.

A different aspect is that when putting leds in series you are in need of a current source and not a voltage source. That also make is for the non professional user more difficult to handle ledstrips with series connection.