SRAM uses multiple transistors and takes up a lot more space than DRAM so it is inherently more expensive because it needs more area. The advantage is that it is fast and doesn't need refreshing like DRAM does. You can also put it on the same die as your computation logic which is technically possible with DRAM, but kinda silly since you need an optimized process to get the best out of that. This process is then quite bad for high-speed logic.

Do you think the price of including SRAM might be reduced somewhat if the big foundries optimize for including lots of SRAM in these types of ASICs?

Unlikely. SRAM is already used heavily in ASICs today and lots of R&D goes, and has gone, into optimizing it already.