I'm no cessationist, but I find your claim regarding verse 7 completely without merit. Verse 30 states a rhetorical question "Do all speak in tongues?" The clearly-implied answer is "No." In context it is clear that the manifestation of speaking in tongues is not given to all Christians, and therefore doing so should not be used as any sort of test for salvation.That's right. People who are born again can operate the other manifestations of the gift of the Holy Spirit as well. But speaking in tongues is one of the few manifestations that every Christian can do at will.
But every Christian has the ability to speak in tongues (1 Cor 12:7), and God wants all Christians to do so (1 Cor 14:5).
As for 14:5, it has Paul saying that he wished that all believers spoke in tongues, not God. It doesn't support the idea that all Christians "can" or "should".