It can't run because your Mac Pro only has a 32-bit EFI. This is not an excuse for Apple for not making it work; I'm just noting the actual technical reasoning.
However, the simple workaround (if you have a Yosemite-compatible video card) that doesn't involve a Hackintosh-level install is to use a modified boot.efi file that thunks EFI64 calls from the 64-bit OS X kernel to the EFI32 firmware of your Pro. Look at the first post of this thread
and navigate to the section quoted below.
Another simplified installation approach is to use a second Yosemite-supported Mac and install Yosemite to the 2006/2007 Mac Pro's drive. This may be done either by attaching the 2006/2007 Mac Pro's drive as an external drive by placing the 2006/2007 Mac Pro in target disk mode or otherwise mounting the 2006/2007 Mac Pro's drive to a Yosemite-supported Mac. Then, after installation, copy Pike's EFI32 boot.efi to that drive's
/usr/standalone/i386 and /System/Library/CoreServices/ directories overwriting the stock Apple EFI64 boot.efi and repair permissions. That drive should now be bootable on a 2006/2007 Mac Pro
I'm typing this from my Mac Pro 1,1 (with an ATI Radeon HD 4870). I used a different Mac (recent Mac Mini) to install Yosemite to a drive, copied the updated boot.efi file, installed the drive into my Pro, and I've been good to go ever since.
That will only work if the chief legal counsel believes the odds are against them.
We're in IT; the odds are never in our favor.
Of course much of this about Apple adopting webkit2 for Safari all pure speculation, but then it has to be when you are talking about a closed source product like Safari and don't work for Apple.
WebKit2 is already used for Safari (desktop). At some point in the future, it is presumed they'll use it for iOS Safari as well.
"Ahead warp factor 1" - Captain Kirk