The thing about TOS was that a lot of the established Star Trek concepts were being invented as they went along. Some things were altered as the series was taking shape--Starfleet and the Federation were among several concepts that weren't there in the beginning, but they became retconned in later as being such as the Star Trek Universe became more established. It's easy to look at TOS and say it contradicted itself at various points in the beginning, but TOS was very much a work in progress back then. It became more cohesive later on, IMO.
But some initial TOS concepts weren't so readily dismissed after the series ended, while others were. The United Earth Space Probe Agency (which eventually was renamed Starfleet Command) continued to appear after those early TOS episodes in both VOY and ENT, and lasers were continued to be used as weapons--albeit less powerful than phasers--by several alien cultures in various episodes of TNG.