I don't think Gallium3D fixes any "inherent limitations", it's just that pretty much everyone feels that ongoing development, particularly the addition of new functionality, should be done on the Gallium-ported version of Mesa rather than the current one. The limiting factor for OpenGL support was really the lack of a suitable memory manager. As I understand it the Intel driver was the first to pick up a memory manager (originally TTM) *and* integrate the MM into the 3D stack, so OpenGL 2.x hardware support is/was available for certain Intel chips. I'm not totally sure of this but that is my current understanding.
There is a branch of mesa where the "classic" Mesa HW driver model has been replaced with Gallium3D. According to the TG guys I was speaking with recently, that branch also includes 2.x support although I'm not sure if that is only with the software driver ("softpipe") or whether it is actually running on any GPU hardware.
Even if only softpipe is supported, that still puts us closer to a GL 2.x solution since even the softpipe version runs mostly the same code as a hardware accelerated implementation and "switches to software" only at the last minute. Classic Mesa chooses between hardware and software rendering at a higher level, as I understand it.
Take all of the above with a grain of salt since it comes from talking to a number of devs rather than walking through the code myself.
So... bottom line is that we are told that the combination of implementing a Gallium3D driver AND running over a kernel/drm with full memory management will provide GL 2.x "magically". We could accomplish the same by changing the current Mesa code to make use of the memory manager, but most of us feel it makes more sense to jump to the Gallium3D version instead.
The memory management work is still in progress though (airlied is trying to get the Intel version into the kernel now, and the ATI version needs more work), and we are starting to see progress on plumbing the ATI chips into the Gallium3D framework (glisse started it, and MostAwesomeDude is working on integrating LLVM), plus I expect our in-house efforts to swing over to Gallium3D once we have 6xx/7xx code working in the current "classic Mesa" HW driver for the radeon family.