Why not use the most effective non-lethal and cheap weapons instead?
In the first place, because "effective non-lethal" weapons don't exist outside of science fiction.
Less-lethal weapons, as they're properly known, are also much less effective, with many criminals (particularly those under the influence of certain drugs) being almost immune. And they're called
less-lethal weapons because they often end up proving fatal anyway.
You get the "job" done with them too, right ? You immobilize a criminal, send evidences to the police and get justice... Isn't this good enough?
No. That is not (or at least shouldn't be) the primary "job" of the police. Their first duty is to
protect the public, and that means using the most effective means available to immediately stop the threat. If a criminal is actively posing a deadly threat to innocent lives, protecting the criminal's life so they may be brought to trial is secondary to protecting the public, and the police can't afford to risk using less effective weapons and techniques that don't always work.