Because the average fan, or public, have no idea about design, or anthing branding related. On here we are lucky that (mostly) everyone has some idea of design, or at least team history and what does and doesn't look good, that is why we are on a design forum. Joe public doesn't have the same knowledge/experience/understanding.
If they did put it out to the public, the designs would be far worse than what we get. So you can imagine how bad it would be.
Look at what happens with naming teams when people put out suggestions, they are based around their personal opinion, and have no real idea of actual branding, designs would be exactly the same, and the worst of the options would be selected over the obvious "good" designs .