There is "doing your job" and there is doing your job. We are all familiar with people who perform well enough not to get fired but who don't take the extra step. My sense is that many police officers have become this way. It is a terribly hard and dangerous job, and officers are not going to take chances if they don't feel publicly supported. The problem occurs another way: it is increasingly difficult for police departments to fill vacancies because the job does not command the respect that it once did.
Remember too it's much harder to fire cops. It took years to fire the one who did the illegal chokehold on Eric Gardner. Meanwhile, someone in the private sector you can mostly can without consequence.
Not to mention that in literally every other profession in America, you are not considered to be entirely above public scrutiny in the eyes of 30% of the public. Imagine doctors protesting because one was fired for leaving a sponge in a patient, or lawyers going on strike because one was fired for missing a SOL. Better yet imagine the reaction from the "police are infallible" crowd if a teacher refused to teach! We'd never accept that, but should accept cops flagrantly lying and not keeping us safe? That is the issue.