Why register access bandwidth is higher then residing inside CPU cache?
There are slower and faster technologies for memory. And there are technologies for creating bigger or smaller amounts of memory. Obviously a technology that creates slower and smaller memory is useless. So of the useful technologies, the fastest one will always provide the smallest amount of memory, and the ones providing the biggest amount of memory will be the smallest. 

Register memory is smaller than cache, therefore it's faster. It has nothing to do with technology, it is a basic economic principle. If the technology used for cache was faster, it would be used for registers.