The whole thing doesn't make sense ecclesiologically (though that was never my point in the OP...), because the standard proof text I've seen the Mormons offer here (Ephesians 2:20) says nothing about either the continuation of any line of prophets, nor the idea of some kind of prophetic 'office', as Mormonism would have it. If we read Ephesians 2 in context, it becomes very clear that the Mormons simply fabricate this idea out of the barest of threads, in the sense of finding a lone sentence they can isolate and make mean whatever they want it to be (that's the danger of proof-texting: ignoring wider context).
From verse 11 onward we read:
Therefore remember that you, once Gentiles in the flesh--who are called Uncircumcision by what is called the Circumcision made in the flesh by hands-- that at that time you were without Christ, being aliens from the commonwealth of Israel and strangers from the covenants of promise, having no hope and without God in the world. But now in Christ Jesus you who once were far off have been brought near by the blood of Christ.
For He Himself is our peace, who has made both one, and has broken down the middle wall of separation, having abolished in His flesh the enmity, that is, the law of commandments contained in ordinances, so as to create in Himself one new man from the two, thus making peace, and that He might reconcile them both to God in one body through the cross, thereby putting to death the enmity. And He came and preached peace to you who were afar off and to those who were near. For through Him we both have access by one Spirit to the Father.
Now, therefore, you are no longer strangers and foreigners, but fellow citizens with the saints and members of the household of God, having been built on the foundation of the apostles and prophets, Jesus Christ Himself being the chief corner stone, in whom the whole building, being joined together, grows into a holy temple in the Lord, in whom you also are being built together for a dwelling place of God in the Spirit.
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Reading the last sentence (bolded) in the context of the rest, it is very clear that the blessed apostle St. Paul is talking to this specific community about how they were once lost and without Christ, but through His coming and their accepting Him, now they are members of this Church having
been built on this foundation. In other words, it's something that has already happened, not something that St. Paul is saying will be continuously happening or 're-happening'. When you build a foundation and it is strong, then it stays and there is no need to keep rebuilding it, because it cannot be harmed in such a way as to require it to be rebuilt, as Jesus Christ Himself is the chief cornerstone, and nothing can break Him as He is God incarnate.
Also note,
giant aside but hopefully helpful to someone somewhere: grammatically, "been" is the
past participle form of the verb "be", used to indicate what in other languages is called perfective aspect, which is itself used for
completed actions, e.g., "has eaten", "have walked", etc. These are all past participle compounds, and while the participle is a form of the verb and
not a tense, it is not a mistake that it shares the same -ed/-en ending as the past tense verb forms, because obviously tense and aspect go together in this way, as you can tell by looking at the pairing of tense and aspect that you get in languages where aspect is much more clearly displayed in the grammar,
like Russian, where you can tell all of this stuff from looking at the verb forms. It is important to recognize how aspect works when looking at passages like Ephesians 2:20, because even though it obviously wasn't written in a Slavic language, it is using a construction that nevertheless expresses perfective aspect, i.e., it's an already completed action. It is not something that St. Paul is saying
will be the foundation of the Church, such that we should follow forthcoming claimed 'prophets' so as to be faithful to the foundation we have been given. It's what
already is the foundation of the Church, and we are faithful to it by accepting Christ, as the once faithless and lost Ephesians did.