Lucas, Hype Machine pretty much “manages redirects to third party song hosts”. They don’t have all this fancy “pastable URL” technology, but you could build it on top of their site as Greasemonkey script that mashed them up with TinyURL.
In fact, when Hype Machine relaunched with their current vc-funded site lo these many moons ago (fall ’07), they had greatly de-emphasized the ability to listen to the music on their own site to the point of making it quite difficult and were focusing solely on the ability to read snippets of blog posts, with listening left to clicking through to the original page. There was such an incredible outcry from their users that, to their credit, they rapidly retreated, restoring much of the listen-on-site functionality that had been the core of the previous Hype Machine (read their blog posts around this moment, here: http://blog.hypem.com/page/4/ and particularly the very striking contrast between: http://blog.hypem.com/2007/10/whats-new-on-the-hype-machine/ and http://blog.hypem.com/2007/10/so-wheres-the-flash-pop-up-player/ and the following posts; just watch them struggle to convince their audience that hypem is about more than just listening to the songs in the face of the obvious rejection of that idea).
The idea that some other more contemporary technology (such as micro-blog linking or taste publishing) can supersede actually listening to music as the core of a successful web-based music technology, an idea that the labels have pushed had via their all-out war on the actual listening technology of all stripes and we web-devs have accepted in the name of peace and practicability, is why their has been no really large scale breakout music site in this era of large scale breakout media sites. On the web, finding stuff means search. And listening means mp3s and flash. There just aren’t that many ways to combine those technologies, and there, apparently, aren’t any that can both withstand labels’ legal pressure and provide a user experience of any large scale value.