Older cheese are tastier, but a large part of that tastiness has to do with their higher concentration of flavorful amino acids (the building blocks of proteins). In particular, the amino acid tyrosine has a tendency to form small, crunchy crystals inside an old, dry cheese like my cheddar. Simply whisking it on the stove top yields melty cheese that's gooey enough, but it's still got discernible chunks of crystallized tyrosine in it, giving it a slightly grainy texture and appearance.
Like the annoying kids in school who end up disrupting the whole class, there are probably chemical solutions to the problem—something or other I could add to make the tyrosine crystals behave and the whole thing run smoothly, but I'm an old fashioned guy, so my gut reaction was just to administer some good old mechanical beating* with the blender. I mean, it made the fat kid from The Goonies get back in line, didn't it?
The regular blender or food processor worked, but a handheld immersion blender was even easier.