So for example, a 6 feet tall nerdy-looking geek is better than 5' 6" athlete or celebrity? Doesn't seem logical to me.

Could be, depends on the woman and what she values. Celebrities are usually in a league of their own. The way you have to see it, is that women look for a certificate of potential for success (and many other things, but this is one of them). Since being tall is generally desirable in society, it acts as such a certificate. It is definitely not the only trait or circumstance that acts as such, but it is pretty much impossible to fake.

The reason why height is so important, is because it serves as a proxy for strength, potential for dominance, and protective capacity. Women feel safe from the world and other men, when they are with a tall man (assuming they also feel safe from him). The circular effect of this is that tall men are seen as a successful archetype from all the attention and resources they get, which inflates their true sexual value. Probably social media and internet has a big hand in this too.

Athletes and celebrities are famous people who have a lot of eyes on them and thus naturally get more attention.

I’d prefer anyone else over an athlete or a celebrity, regardless of height. Humans are allowed to have different preferences.

No one claimed that height is the only or the most important metric; simply that it is a metric by which partners can be judged.