I'm not saying the tools aren't bloated, but I believe that a lot of the size (sorry, can't quantify right now) are the datasets for each and every FPGA model that the tool supports. This includes, among other things, timing information for every wire in the chip. You really only need the files for the device that you are targeting and you do have the option to install only that, or you can install larger groups (e.g. same family, same generation), all the way up to installing every device that ever existed that the tool supports. That's how you get to hundreds of GB.
Are you sure about that, or is it just a guess? If that is the case, how will the open source toolchains avoid the same problem when they eventually become the industry standard? (I can imagine something like a software repository for serving device-specific information on demand.) Are they planning anything right now?