You answer me under a false assumption. I do not believe Cessationism. I do not believe that spiritual gifts ceased in the Apostolic age. My interest in this thread is to promote a correct understanding of the gift of tongues and a correct understanding of Paul's letter to the Corinthians.
I do not agree with your view that the Corinthian church was ignorant about spiritual gifts or that they had forbidden people from speaking in tongues. Rather, some people were actually speaking in tongues, while other people were doing various other things, claiming to be speaking in tongues when in fact they were not. These disparate acts, all claiming to be the same thing, raised questions in the minds of the believers in Corinth, which is partly why they wrote a letter to him. They had questions about the true nature of the gift and how to understand what is happening.
By the way, when Paul exhorts the Corinthians to prophesy he isn't necessarily talking about the gift of prophecy. What do I mean? He begins chapter 14 with a general exhortation.
Pursue love, yet desire earnestly spiritual gifts, but especially that you may prophesy. 1 Corinthians 14:1
In general, to "prophesy" is to speak by the Spirit of God. (Refer to 1 Corinthians 12:3) There are many different spiritual gifts that fall under this general category: predicting the future is one way to prophesy, but so is teaching, preaching, and evangelizing. All of these gifts fall under the general category of prophesying.
In the verse above, Paul is talking about prophesying in the general sense, including all aspects of edifying the church. The text that follows is NOT a comparison between two spiritual gifts, i.e. tongues and prophecy. Rather, Paul's goal is to draw a sharp distinction between actual tongues and other acts which people have mistaken for tongues. Paul will argue that actual tongues is one of the many means to "prophesy."
If a person is speaking to themselves, this is not tongues, it's something else. Actual tongues is speaking to the church by the spirit of God. In other words, the gift of tongues is another way to prophesy. If a person is praying to themselves or praying in the spirit, this is not tongues, this is something else. And I am not saying it's wrong to pray silently and I'm not saying that praying silently "in the spirit" isn't a valid spiritual practice. I'm simply explicating Paul's view that the actual gift of tongues involves public speaking by the spirit of God. To speak in tongues IS to prophesy.