seems like the average citygoer in Rome or Greece could at least read.

Possibly. We have little evidence for the Greeks outside of Athens, but Athens was really a pretty small city in comparison with the great metropoleis of the Roman world. It seems likely that at least at Athens during the height of the democracy the majority of citizens, though not necessarily the majority of urban dwellers, could read a little bit, and we find for example from Aristophanes that relatively low-ranking individuals could be expected to be able to at least muddle their way clumsily through a few lines. At Rome functional literacy was probably common at least down to the skilled tradesmen, but the vast majority of the urban population were unskilled day-workers who probably had little incentive to read--we have very little evidence one way or another for them. Some estimates of literacy are rather high, approaching 50% or more, but others like William Harris put the rate in the Roman world down around 20-30%, clustered around the Greek centers of education. A point must be made about real literacy and functional literacy. In the ancient world, no matter the literacy rate, the vast majority of people probably could not comfortably read the literary works of the classical corpus. A much larger group of people could read a few words here and there, and probably write their own (and others') names. But complex literary works were out of the question, and there's some debate as to how many people were even able to read inscriptions. See, evidence like inscriptions or graffiti is not particularly useful. Inscriptions are generally monumental in nature, and the actual text written on them is not necessarily particularly important. How many people today can understand the inscription on the pediment of the Pantheon, "M. Agrippa L. F. Cos. Tertium Fecit?" Even if you can read the letters how many of us necessarily know that that it means "Marcus Agrippa, son of Lucius, built this in his third consulship?" Yet that doesn't really matter, does it? Same deal with other inscriptions, if you can read enough to make out the important parts (i.e. names) that's nice, but it's not actually necessary for the inscription to have its effect, and doesn't necessarily imply a need for literacy. This is the problem we're faced with.

Now, of course, even William Harris' low estimate is considerably higher than any literacy rates in the Middle Ages that I've encountered, but the point is that literacy in antiquity is rather deceptive