The x86-64 instruction set adds more registers and other improvements to help streamline executable code. However, in many applications the increased pointer size is a burden. The extra, unused bytes in every pointer clog up the cache and might even overflow RAM. GCC, for example, builds with the -m32 flag, and I assume this is the reason.
It's possible to load a 32-bit value and treat it as a pointer. This doesn't necessitate extra instructions, just load/compute the 32 bits and load from the resulting address. The trick won't be portable, though, as platforms have different memory maps. On Mac OS X, the entire low 4 GiB of address space is reserved. Still, for one program I wrote, hackishly adding 0x100000000L to 32-bit "addresses" before use improved performance greatly over true 64-bit addresses, or compiling with -m32.
Is there any fundamental impediment to having a 32-bit, x86-64 platform? I suppose that supporting such a chimera would add complexity to any operating system, and anyone wanting that last 20% should just Make it Work™, but it still seems that this would be the best fit for a variety of computationally intensive programs.
There is an ABI called "x32" for linux in development. It's a mix between x86_64 and ia32 similar to what you describe - 32 bit address space while using the full 64 bit register set. It needs a custom kernel, binutils and gcc.
Some SPEC runs indicate a performace improvement of about 30% in some benchmarks. See further information at https://sites.google.com/site/x32abi/