I agree totally with what Nathan Natas said. Having been an employee of a company who constantly hired and kept bad employees I know how it breaks down the moral of the whole team.
If the company I had worked for would have kept to higher standards I would probably still be there but I got tired of being the only one in my department that actually did work and showed up on time and stayed in my department and worked during my scheduled working hours!
You did everyone including yourself a great service, hard to do but then who said life is easy? LOL