Well the thing to remember is that exile is a punishment for the elites. You need money/wealth to be able to just pick up and go live in another state/city. And if you're one of the elites, you're well known because you were politically active. For Athens, ostracism was (in theory) to remove any politician who became too popular and thus a risk to the democracy. That kind of person is unlikely to be able to sneak back in unrecognized.

Firstly, if a Roman politician was exiled, it was often because they chose to go into voluntary exile to avoid a death penalty. Cicero is an example of this to avoid his conviction for the execution of Roman citizens without trial during his consulship: if he'd stayed in the city and lost his trial, he could have been executed. If he had returned to the city before his exile was legally overturned, he could also have been executed.

Secondly, if you're a rich man like Cicero, do you want to sneak back into Rome and live undercover for fear of being recognised? Or do you want to live in a decent house in relative comfort with your servants and perhaps family? If a man of Senatorial rank thought being exiled and sneaking back into the city to live under a rock and hoping he doesn't get discovered and thrown off the Tarpeian Rock was a good deal, then he was probably too mad to live anyway. A lovely country villa where you could do whatever you like was much better.