There was a portable TRS-80 (
https://en.wikipedia.org/wiki/TRS-80_Model_100) that used SRAM, however this looks more like based on the original B&W TRS80.
SRAM had a significant price tag, and only got low power in the CMOS versions. The CMOS versions were really low power, but AFAIK only available later.
With all the interfacing / refresh integrated in the 6883 (= 74LS385) it is easy to use DRAM. So this simple looking 74LS... is a really important part for the CoCo - it's the chip that holds things together. The whole circuit looks a lot like the typical circuit in the 6883 data-sheet.