The popularity is indeed an odd thing, because the prices aren't that much different to Mcdonalds and Burger King, and even though they are really fast with giving you what you ordered, you can often wait ages to get to the front of the line (inside and the drive-thru).
Maybe it is just the taste... which I don't recall as being too spectacular either.
It could also be a tourist drawcard as well, because for a long time the business refused to sell franchises or expand beyond California so that they could control the standards and quality, but are now looking to expand into the rest of the country, slowly.
Another reason could be that they are known to pay above the minimum wage, making them a sought after place to work, earning customer loyalty to a business that is loyal to its workers.
They are famous for having a small (regular) menu, so for creatures of habit, there isn't much to process or think about when deciding what to have for lunch or dinner.
And their "secret" menu is probably the novelty that attracts other people, but the times that I've been at one of these places, I only ever saw people eating or ordering the regular menu items.
This was from 2014, so prices may have changed since then.
That's the exact same things I ordered, back in 2014....
I've been to the one that's two blocks from the main Hollywood walk of fame once in 2014, and the one just outside of the LAX airport in 2010 (despite it being so close to the airport and having the chance to go in there several times since 2010, it has always been too crowded with people and cars, so I never managed to go back there).
This was the Hollywood one, which like the LAX one, was always full of cars in the car park and drive-thru (there are about 30 cars in the drive-thru queue here, and the entire time I was there eating, the line of cars would constantly be all the way out onto the road)...
Make sure you try out Wendys if you can, as they have some really nice burgers (including the Baconator). Also Carls Jr (for the American Thickburger), Fatburger, and Arbys if you come across them.
IHOP is also really nice too.