Police are trained to lie to you in the course of investigation so “they could choose not to do their job (by conducting an investigation)” doesn’t refute the notion that it’s their job to lie to you, it affirms it. It’s like saying “it’s not cops’ job to lie to you, some of them are dogs whose entire job is sniffing out cocaine with their extraordinary sense of smell”
It's like saying it's a pilot's job to wear a uniform. The uniform may be required by their employer, but it's not the job. A law banning pilots from wearing uniforms would not result in jail time for doing their job.
What are you talking about? You asked “how is it the police’s job to lie to me?” and got an answer (it is). It’s not a hypothetical that relies on a thought experiment, it’s just a true statement. You can’t imagine your way into a world where it’s not the police’s job to lie to you.
Lying is not an inherent part of the job nor is it required by all employers. It is not, in fact, the police's job to lie to me, any more than it's a pilot's job to wear a uniform.
Making it illegal for police to lie on the job would have the effect of many police no longer lying on the job, rather than putting all police in jail.