Why is there demand for random gear drops on the player market?

I've played this game on and off for over four years, and no longer have a single character that is below level 80. Once you get to that stage, you'll find that your drops are almost all level 80(ish) drops, which means that when you salvage them, you'll get only high-level (T5 & T6) materials.

So the best way of getting lower-tier crafting materials (which you need in large quantities for some high-level recipies) is to buy them outright or to salvage them from drops you buy. Once you realise how (relatively) expensive those materials are, you'll find that the gear is cheaper to buy, and if you're going to salvage it for materials anyway, "horrible stats" don't really matter.

(As for your side question: there are countless websites, such as spidy, that will show you all that information, plus of course you can use the trading post itself to search for gear in a certain range. If it exists in the game, those websites will know about it and it'll be listed on the TP.)

Amos M. Carpenter's answer is all about the level 80 point of view. Mine is not: not everyone insta levels to 80.

If you go in lower level areas, you'll see that they are not dead. People are still levelling in them. I've levelled two characters in the past month. One because my revenant was still level 20 and another one because I'm bored of changing my stuff from pve to pvp, so I made a duplicate pvp-only character.

When levelling a character I buy him a new set every 10 levels or so. This way, I don't lose too much time fighting. I usually make my buy orders 10 levels in advance. So when I reach level 30, I put on my new gear (blue or green, though blue is often cheaper) and put orders to buy my level 40 gear. It's always fulfilled before I get there. I know some people who buy new set of gear every level or two.

When a lowbie, while I know the general tactics and the timing to evade mobs, I don't especially know the class I'm playing. I'm taking hits harder than a level 80 and I can't recover from them as easy as a level 80. Up-to-level gear helps me play the game better. So I need to get it from somewhere. The trading post is my main source. And I sell as well the gear I drop but don't need.