What do you think the Media folder is to be used for?
Do you put your images in there that are used in many places across many websites? Or do you put every image in there, no matter if it only sits with one document buried deeply in one website?
What about style sheets or javascript files that may be shared broadly?
Do you stick audio, video, pdf, excel and word documents in there?
How is it different to a normal folder that may or may not be within a site asset.
Just wondering how it is intended to be used…
Would it be facetious of me just to answer "Yes"? 
It can be used for any and all of those things. The difference is that the Media folder gets a URL automatically – but you need to remember to add additional URLs to the Design, Media and Users folders if you add additional root URLs to the system.
My guess is the media folder was developed because they took the easy development option in not implementing an Asset Library like various other products (e.g. RedDot CMS and various other OpenSource CMS packages I examined).
An Asset Library is 100x times better than an Media Folder - however, at least this is a start I suppose…
The WHOLE of Matrix is an Asset Library. What more do you want?
I was playing in RedDot CMS yesterday - different terminolgy. In a different way of wording they have a media library that lets you catalog all your media into a browser which automatically shows a thumbname for each of the images etc and also lets you add a caption. This way when users need to select an image they open the image/media catalog and just scan through all the thumbnames in the book for the image they are after. This is heaps more simple that looking at a list of names.
Several of the other OpenSource CMS packages have this feature.
In Matrix v3.6 (currently our development branch) this will be pretty simple to implement using the new features within the Image asset and the enhaced Asset Listing engine.
Gosh, take it easy. The Media Folder is not a replacement for an Image Library and it is certainly not an "easy way out".
The reason it came about is very simple. We needed site designs to be web accessible because of new changes to design linking. This meant users would have to move all their site designs to a new Site asset (or somewhere else they could be web accessible). So we created a Designs Folder that is web accessible by default and available as soon as the system is installed.
Recent changes to the User assets have also made them web accessible, so we decided on the Users Folder as well.
The Media Folder was the other logical choice. Drop all your site media in there and it will be web accessible without you having to do anything.
These folders are simply shortcuts because some people find it hard to organise their data. For new installs, it makes it easy for users to decide where to put new assets.
As for the image library, I'm sure one day it will come - but the Media Folder is not for that purpose and there are many more features that have been added to our current DEV version that provide a lot more value than an Image library.