Funny how JTAG these days is synonym with in-circuit debugger. The original use of the port was to support IC interconnect testing, and for high density boards it still is. For external parallel and serial memories you can use the boundary scan registers to bit bang the pins and read the inputs. In fact, that was a popular way to program external memories on fresh boards if they didn't come with embedded bootloaders.

Even if you don't have the scan configuration file of a particular chip for your tool, they are very standard and easy to figure out. No desoldering required!