SRAM has actually been used, off and on, over the years, as main RAM, typically for special-purpose computers. The main advantage of SRAM is being able to request different addresses quickly. Actual transfer rates have rarely been much faster than DRAM, if at all, because the memory bus gets in the way, including lines on the PCB and on the chip affecting the speed of access (caches are fast because they're close, directly accessed, and can be tuned for the processor using them). And, that is at least a decade old--with everything getting smaller, thus making capacitance and inductance more of an issue, I'm inclined to think that Tuna-Fish is right about SRAM being slower, when used off-package.
Nintendo, Microsoft, IBM, and now Intel, have all gone to using nearby DRAM as a performance-enhancing near memory (in IBM and Intel's case, only as an added level of cache). Just having speedy DRAM arrays right next door, that don't eat into the main system RAM's IO, can improve performance more than a smaller amount of SRAM, mainly by increasing the data density. Having the RAM really close, not separated by a bunch of external wires, makes the difference. The wires between your CPU and the memory chips are a big deal. Just going off-package forces them to be hundreds of times the length of on-package, which is then also so much more than on-die.
If RAM could be made 4 or 5 times faster, there would be a big market for it. CPUs might take a few years to be adjusted so as to make good use of it, but it would happen. Today, though, much of the problem is that we're pushing physical limits, and they just don't give easily.