Cat5e is good for 125MHz clocking, Cat6 goes up to 250MHz, and DVI needs up to 1.5GHz clocking. However with better cable and short runs, you can probably get away with using an RJ45 that everyone can crimp themselves.
The real reason why DVI and HDMI exists is to generate income for the creators of those specs. It costs in the area of $10K-$15K to put the DVI and HDMI logos on the front of your settop box, plus some small change per unit shipped.
There are literally hundreds of pointless specs out there with licensing schemes just to generate revenue for the creators. Digital Design Working Group, the authors of the DVI spec, got lucky and were able to persuade equipment manufacturers to design it in. It had some momentum from the PC w/ LCD display market as well. I wonder if they had to give away a couple key accounts like to Sony to ensure it's sucess.
Overall, it's not very robust, nor applicable for home theater. I think the industry would have been better off if they scraped DVI/HDCP/HDMI and created a fiber solution.