That's not the point, the SA badge tells someone your answers, traditionally, are reliable. It's not saying that they may be reliable or that there's a higher probability that they are reliable, it's saying this person has a 100% verifiable ability to give accurate answers.
Imagine you're hiring someone to test high voltage diodes or something for your company. Let's say you have some new applicant with a Masters degree and no work history. Then someone comes along who has been testing diodes for 15 years and you've called up his previous employers and they say they're great, but he never went to college or you for some reason can't verify his degree. Sure, there's a very good chance the guy with the MS can do the job, but the guy with 15 years experience is guaranteed to know how to do the job.
Same situation here, except for the fact that you can say you have whatever degree you want and no one will have a clue. Outside of a few members here who have purposefully divulged such information over the years, anyone could say anything with no proper way of verifying. And you say that someone will get caught at some point based off their answers, but that practically argues FOR the method that exists right now. Verification based off results.