As to the text... Paul never said that the ability to speak in an unknown tongue was for the edification of the assembly. On the contrary, he said just the opposite.
The interpretation of tongues is for the edification of the assembly. But you can't have the interpretation of tongues without the words spoken in tongues. 'Divers tongues' is listed with interpretation of tongues among the gifts given to members of the body of Christ 'to profit withal' or... 'for the common good' in another translation.
Btw, the verse that follows is not 'just the opposite' of edifying the assembly. Tongues has multiple functions. Serving as a sign to unbelievers is only one of them.
1Cor 14:23 If therefore the whole church be come together into one place, and all speak with tongues, and there come in those that are unlearned, or unbelievers, will they not say that ye are mad? Paul taught that speaking in tongues was for self edification: 1Cor 14:4 He that speaketh in an unknown tongue edifieth himself; but he that prophesieth edifieth the church. Thus, Paul always magnified the preaching/teaching as the way to edify the assembly:
Look at this in the broader context. Paul is explaining how tongues functions as a sign, fulfilling 'With men of other tongues and other lips will I speak unto this people; and yet for all that will they not hear me, saith the Lord.' When unbelievers hear all speak in tongues their reaction, in Paul's example, is to say 'ye are mad.' Compare with the accusation of drunkenness in Acts 2.
Also, look at Paul's conclusion about what to do in church, nay, commandments of the Lord. He says when ye come together, every one of you hath a psalm, hath a doctrine, hath a tongue, hath a revelation, hath an interpretation. Look at verse 26. Verse 27 and 28 specifically allow speaking in tongues and interpretation in church. Speaking in tongues combined with interpretation edifies the church and the Lord specifically allows it in church if done in an orderly manner in this passage.
I do wonder about your assertions. Have you bothered to sit down and read the passage carefully?
1Co 14:5-6 Now I would have you all speak with tongues, but rather that ye should prophesy: and greater is he that prophesieth than he that speaketh with tongues, except he interpret, that the church may receive edifying. But now, brethren, if I come unto you speaking with tongues, what shall I profit you, unless I speak to you either by way of revelation, or of knowledge, or of prophesying, or of teaching?
Notice 'except he interpret'. The passage encourages interpreting speaking in tongues, prophesying, or saying other edifying words to the congregation. (Also, notice the underlying assumption is NOT a church meeting where one pastor does all the speaking or even a group of elders does so, but members of the body of Christ do such things as prophesy and speak in tongues and interpret in church.)
The four preferred methods of edification: Sharing a new found revelation with others. Sharing your acquired knowledge with others. Preaching the Word to others and Teaching.
It is conceivable that Paul was describing the types of things that could be said in an interpretation of tongues. Look at the context.
Paul never placed speaking with tongues high on the priority list of important gifts: 1Co 14:18-19 I thank God, I speak with tongues more than you all: howbeit in the church I had rather speak five words with my understanding, that I might instruct others also, than ten thousand words in a tongue.
He does not say where tongues ranks when compared with leadership or service or other gifts. He spends part of chapter 12 instructing his readers not to despise other members of the body, which have certain gifts. So we should not do so with speaking in tongues or interpretation.
Also notice that Paul spoke in tongues more than all of his readers, so his attitude toward it is not negative. A theme that runs throughout the chapter is that speaking in tongues without interpretation does not edify the assembly, and the rules set down for it are for the context of the assembly.
Finally, we know that the Corinthians were being childish over these gifts, with much envy and strife. Paul gave this warning to them to grow up: 1Co 14:20 Brethren, be not children in mind: yet in malice be ye babes, but in mind be men.
Can you show me one verse in I Corinthians that indicates that there was either envy or strife about the gifts? Paul's correction here is related to their childish understanding. He apparently considered it childish for them not to realize that listeners had to understand what the message in tongues said by means of interpretation in order for it to be edifying to them.
He then specified the purpose of the gift of languages.
This is very limited thinking, and not in line with scripture, that tongues as a sign is THE purpose of tongues. What do we do with the rest of what the book has to say about the topic? In chapter 12, tongues and interpretation are among the manifestations of the Spirit given 'to profit withal.' In Chapter 14, tongues edifies the speaker, and if it is interpreted, it edifies the congregation. In verse 26, tongues is allowed as a type of utterance that may be spoken 'unto edifying'. Verses 27 and 28 give instructions allowing interpretation of tongues in church. So why would only one part of the passage be THE purpose for tongues and not the others?
First they were to fulfill prophecy of the OT: 1Co 14:21 In the law it is written, By men of strange tongues and by the lips of strangers will I speak unto this people; and not even thus will they hear me, saith the Lord. Secondly, they were for a sign to the Jews and unbelievers: 1Co 14:22 Wherefore tongues are for a sign, not to them that believe, but to the unbelieving: but prophesying is for a sign, not to the unbelieving, but to them that believe. Believers have no use for this sign but don't many charismatic churches today quietly criticize those who cannot speak a tongue?
Tongues are a sign for unbelievers. For believers, tongues is one of the gifts of the Spirit. Tongues edify the speaker. One who gives thanks in the spirit, speaking in tongues, gives thanks well. Combined with interpretation, speaking in tongues edifies the assembly. I Corinthians 14 specifically allows it in church and commands 'Forbid not to speak with tongues.' So the church does have a use for speaking in tongues besides it being a sign to unbelievers.
Are they, like in the Corinthian church, seen as inferior? This has been my experience with the Charismatic movement.
Paul does not say that Corinthians who spoke in tongues considered themselves inferior to those who did not. Some Charismatics do believe in the 'initial evidence doctrine'-- that tongues necessarily accompany baptism with the Holy Spirit (seen as empowerment subsequent to salvation.) I do not agree with that, but I cannot say I have heard Charismatics criticize someone for speaking in tongues.