>"Even if signals in the chip were moving at the speed of light, a chip running above 5GHz wouldn't be able to transmit information from one side of the chip to the other".
That's almost completely misleading. Except for the clock itself, nothing that happens inside a processor takes a single clock cycle. And clock distribution delays need compensation anyway.
That's also true of memory. No one has ever seen 1-0-0-0 CAS RAM. (And no one ever will.)
It's true that pushing up against distribution times makes topology more complicated and lowers the maximum possible speed.
But that's actually the difference between electronics and photonics, which promise to run many orders of magnitude faster than EM-based silicon design. (I've seen "millions" quoted, but that may turn out to be hyperbole. Even so - optical fibre can run at tens of Tbps.)
Of course there's a difference between transmission speed, which is a function of the speed of light, and maximum data rate, which is a function of bandwidth.
But unlike electrons-in-silicon connections, photonics may not need to be 100% serial. It's entirely possible to get multiple data channels down a single line with frequency multiplexing, and perhaps also by phase rotation.
That has huge potential to change the packing density and the speed of processor designs; potentially you could have processor elements that were massively parallel but connected with single lines.
There's also some hope that because power dissipation shouldn't be such a problem, it will be easier to make 3D designs - although that's probably more speculative.
Bottom line is silicon is nearly done, but photonics is just getting started. Like fusion power it's probably a couple of decades away, but when it arrives it will be huge.