Not really, SRAM(what most caches use) isn't just more costly is also consumes a lot more power. You'd be hitting thermal limits much sooner than with traditional DRAM.
I don't claim to be an expert so there are probably cases where it's lower. However when I was looking into fast RAM for storing data from an FPGA for a simple Logic Analyzer most of the SRAM was almost 2-4x what DRAM was for power consumption at the same storage size(with SRAM being a blazing fast cycle access).