Basically the same reason why you have an Audi (A8?) as your avatar as opposed to a Honda Accord. They both will do the job, and quite well I might add, but the Lian Li cases have an extra amount of "umph" when it comes to making your computer about style and less about function only. The Lian Li cases will have much of the features that other case manufacturers do, and, as you mentioned, I hear they do have exceptional build quality. Another aspect of Lian Li cases is that they are usually made out of mostly aluminum, and not steel like most other cases. This gives you the real brushed aluminum look instead of just plastic with the facade of brushed aluminum (like my PS07
). This also makes the case deceivingly light!
Lots of people also purchase them because they are "classy" (best way to describe it), and not too "gamey" and gimmicky. On their bigger cases, they offer lots of free canvas space for mods and customization.
At the end of the day, people will pay more for what they think is best for them, and what suits their taste. I wont deny that some sub $50 cases are very well built and are overall a great build space though, I bought a NZXT Source 210 for my folding rig, and I really enjoy it!
TL;DR- Style, Build Quality/Materials, Customization:D