On the other hand, the format does not appear to actually be that complicated, so integrating the SDK probably wouldn't save that much programming time compared to just reimplementing it.
Let's say it is Autodesk's fault and they don't care. Now what? Blender is the tool that's a pain in the ass to use so the onus is on them to make their tool not suck. Meanwhile the rest of the world will continue to use FBX because it's an awesome format to work with.
You are the one who was all "GPL hurtz dem users!!"
You're probably right with your assumption that FBX is awesome, but this wasn't part of the debate.
Free Software's there for a reason. Let's not forget that. And if we stick to that (i.e. not trade freedom to whatever feels comfortable at the moment), there's a good reason to not use LGPL instead of GPL: http://www.gnu.org/philosophy/why-not-lgpl.html