If there isnt already a website that lets you just upload a large image and then creates all the different sizes for you and provides the code to paste in for you then there needs to be. If it doesnt exist and people here are interested, i'll make it this weekend.
The only caveat is that a good large icon does not necessarily make a good small icon. Icon designers will do each size by hand to make it fit the format, getting rid of extraneous detail along the way. It would be difficult to model this actual process. But, for a quick and dirty process to get something running without paying money, a site like this would indeed be useful. There are plenty of favicon generators, but nothing for the modern age.
The author of the posted linked to this site which does some of the sizing conversions: http://www.xiconeditor.com/ but the tool you describe (and hopefully will create) would be much better.
Allthefavicons doesn't win it for me from xiconeditor. I need to be able to retouch the shrunken icons, on this pixel level whatever image you'll put in will most likely look a bit quirky.
I think I remember seeing a similar tool on Reddit a few months ago. I tried to Google for it, but couldn't find anything so perhaps it's not around any more.
Either way, it'd be a very handy tool so I say go for it!