Is there a strong cryptographic reason for GCM's 2^39 - 256 bit limit?

In reading through the original GCM specification (McGrew & Viega '05), the composition of the 128 bit Initialization Vector as a concatenation of a 96b nonce and a 32b unsigned wrapping counter seems arbitrary and forces the scrambling pattern to repeat every 2³² 16-byte block.

Is the algorithm expected to be secure for significantly longer stream lengths if for example the IV were a 128b nonce XORed with a 64b or 128b counter, or are there known cryptanalysis issues that begin to arise?