Wrong. You’re still not getting it. Try looking at what the recruits have to go through…even try to see if you can qualify yourself, just for the heck of it.
As for the physical portion, that is just one part of the process. The psychological/IQ test is a big part of it, as is the background check. And then there is the oral interview where you have to sell yourself (this is the only portion of the test that has something in common with most private sector jobs), and where the hiring committee/HR makes further notes about the candidate’s mannerisms, aptitude, background, and emotional/psychological state.
Yes, there is an IQ/psychological exam for many of these pubic sector jobs. I know it doesn’t fit into your (extremely uninformed) conceptions about public service, but most public agencies only higher people with above-average IQs (but not so high that it might indicate the potential for “unusual” behavioral or thought patterns).