Like I a said. The iPad can't download folders (collections of files). Only individual files. This is because each file needs to be saved to an app that is compatible with that file type. While your folder may contain only files compatible with the apps you want, the Safari has no way of knowing this; so it won't download the folder.
On a computer, even a Mac, you are downloading to a general file system. It doesn't care what the file type is until you try to open it.
The root of the problem is that computers are file based. They work with files. They don't care what the file type is, so they will download, move, copy, whatever, a file anywhere you want it. The type of file is only important when you try to open it.
iOS was designed around apps. Files only exist within apps. Because of this all the files in an app (usually) need to be compatible with that app. You can check this with an individual file, but the nature of folders means they can contain any number of file types. That means allowing Safari to download a folder and save it to an app (because Safari on iOS can't save files to itself) would let you upload incompatible files to apps. So the easiest solution is not to allow it.
I'm pretty sure this will change as new features are added to iCloud Drive. It's already possible to create a folder (on the Mac) in iCloud Drive and place any kind of file you want in it. Then you use an apps' access to iCloud Drive to look at the folder. Of course, you can only open compatible files, but you can at least see the folder.
But iCloud Drive is new, and still lacks a lot of features that are present in a full file manager.
There are apps that act like file managers (within the app), and it might be possible to download a folder there. I've never tried. GoodReader is the best bet. It has a built in browser that you can use to navigate to the folder, or you can enter the folder's URL directly. Last I checked it was on sale for 99 cents. Again, I have not tested this. I make no promises. However, GoodReader is a pretty handy app to have. It's supposed to be a PDF reader/annotation app, but includes a lot of other bells and whistles. We commonly call it the Swiss Army Knife of apps.
Oh yes, GoodReader is also capable of downloading and unpacking .zip files. So even if it can't download a folder directly, it can still do that.
The thing to understand is that iOS started out as a far simpler OS that a full computer. To make everything secure and fast on the less capable hardware Apple limited what it could do. As the hardware has gotten better, and the devices more popular, Apple has added a lot of capabilities; but they don't just add stuff for the sake of a feature. They're still concerned with performance, ease of use, and privacy and security. As a result a lot of feature we take for granted on more traditional computing devices are either missing, or require a different approach.
For many people the iPad is still not a full computer replacement. But it's a lot closer than it was when it launched.
