256-bit and wider data busses are also common in CPUs and GPUs but that's just for data throughput.

The important question is,  would the extra transistors needed to create a 128 bit word, offer more processing power than just using them to produce a second core?   Both offer an improvement,  which offers the highest improvement?

16-bit colour encoding for each pixel is sufficient for photo-realistic picture. If we calculate GPS position in 40 bits we can have  precision of 1cm. 64 bit is enough for nearly every engineering, science or business calculation. Mind you, we can still use 128 or 256 bit numbers in programs in same fashion as old 16-bit 8086 handled 32 and 64 bit numbers. Finally, after fighting 64kB data size limit on early PCs and 4GB at 32 bit few years ago, we are now at ease for few more decades.

The gradual move to 64 bit had practical reasons. 32 bits can access 4GB of RAM and the OEMs were prudent enough to switch from 32 bits before computing approached that wall.
There is just no reason to do 128 bit computing

Sadly, most consumer hardware is technically still 36 bit limited (again due to memory restrictions)

18 quintillion is big enough for nearly every serious practical and impractical use case. Only encryption uses bigger numbers, and those are fine on the slow path.

Intel/AMD x86-64 variable length instructions (incl prefixes, immediate/displacement) means the instructions can be upto 15 bytes (120b long). SIMD/Matrix maths can be 512b long for Intel/AMD. ARM supports longer data arrays only via looping with the SIMD engine effectively executing multiple internal instructions (despite code having 1 instruction).

Even at pcs we don’t need anything beyond 64 bits

128 bit was never predicted by anyone who developed low level libraries or OS software which could need it.  There are niche cases in crypto or simulations that might benefit.  But given the circuits still scale quadratically it is not surprising 64 bit was very much a challenge and where scaling by software took over.  This practical word size limit has countless engineering reasons behind it.  Specialty hardware could still implement 128bits.  Ive done it on an FPGA even.  But general purpose hardware is unlikely with even the current state of the art fabrication tech

While the information provided in this video is solid and good, the title is misleading.
In a way, 128bit,  256bit and 512bit are here. (Just different than initially expected).

As pointed out in the video, the real driver to increase the "number of bits" was
accessability of address-space. And here (as also pointed out) we have reached
a threshhold with 64bits where we still only use a fraction of the space available
after all these years. ... But ... processing of data is a different story ... there is no real
need for super-long integers or floatingpoint numbers ... the 64bit "long long int" and the
64bit "double precision float" do serve most needs of today nicely.

So, why do I write that 128/256/512 bits are here? ... the buzzword is
"SIMD" (single instruction multiple data) ... we can process multiple smaller elements of
data with a single instruction in parallel (and we thereby speed up computation of
otherwise complex things). MMX, 3dNOW, SSE, SSE2, SSE4, SSE4.2, AVX128, AVX256, AVX512
all these are extensions to the instruction set that apply the single instruction to more
than just one set of arguments. and by handling 4 64bit units in parallel, we are handling 256bit
in a single instruction (or 8 64bit units handle 512bits in a single instruction) ... and in the moment
this is the only side that needed the extension of bits.

How do BogoMIPS apply here, or to quantum computing?

CPUs and GPUs did become 128 and even 256 bits. Look at the bus sizes, SIMD instructions. It's just that 32 bit and 64 bit operations are too useful to relegate to and edge case.

"As memory got cheaper."

How about the nanometer processing nodes for microprocessors? Or the generations of wireless technology in cellphones? It seems most good engineering intentions turn into useless marketing jargon.

this is all very fascinating but dont you think sony may have been reffering to the GPU side of the chip not the CPU side?

Thanks to the decision not to make 128 bit the next standard for general purpose computers, we are still able to use computers more than 15 years old for modern tasks. It was a good decision.

because it was designed for a bigger chip that was for a bigger pc.   like the size of two desktop towers.  size shouldn’t matter

You've broken your principle.  The 8080/Z80/6502 etc.  were considered 8 bit because their primary registers were 8 bit.  Their address spaces were all 16 bit.  By your paradigm, all of these 8 bit processors would have been considered 16 bit.

yeah, I figured out 64 bits would be the end for a long time to come a while ago
more processors yes, bigger busses? naw. Addressing and memory was always the issue

" That Never Came Through "