The chrome lining was done to significantly increase the service life of the barrel and to reduce corrosion in some environments. Prior to the M16, chrome lining was only used on machine guns due to the volume of rounds that went through them.
Far more rounds were put through the M16 by soldiers than prior weapons like the M14. Despite the chrome lining, M16 barrels still wear out over time and have to be replaced.
"in some environments" being the Vietnam war the US was involved in, in reaction to casualty reports where a large number of men were killed with their rifles broken down for repair likely due to mid battle stoppages.
And the same applies to number of rounds: the entire point of a 5.56mm cartridge was to give soldiers more ammo so they could sustain volume of fire in the field: it was a design goal.
If design changes fixed a serious flaw with a weapon, then it was a flawed design.
Far more rounds were put through the M16 by soldiers than prior weapons like the M14. Despite the chrome lining, M16 barrels still wear out over time and have to be replaced.