Strangely much of what you have written Catholics and Orthodox would accept, but they would apply that to how the early church was run!
The Lexicon of the Timothy word is worth checking out the Greek uses a term meaning "profitable" or "useful" to describe scripture but does not necessarily use any words for "all sufficient" (and the mechanics of saying something like that did exist since Greek is a pretty articulate language.) Some Catholic apologists I have read make the apt point that if you read on other subjects like prayer or fasting the Bible says very similar things in regards to them, but it would be a stretch to say that for spiritual maturity all you need to do is to pray or fast! But if you understand the passage in its context it makes sense for the language used. At the time it was written, it was speaking of the OT, it was mentioning how the OT is useful for NT preaching (since as we previously discussed the NT was currently being written and not called "scripture" by early Christians until centuries later when they were all bundled together in the first Bibles)
I actually find the story of the "noble Bereans" of the Book Acts very instructive on issues like this!
1. I had a feeling they would only apply it to the early Church.
2. I agree, the word profitable does not mean all sufficient but when we look at the context and the surrounding words, along with comparing it to the rest of Scripture(this includes the books written down by the apostles), we see that it is indeed saying that the scripture given is all sufficient.
When timothy says "16
All scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness:
17
That the man of God may be perfect, thoroughly furnished unto all good works." We see that he says first that all scripture is given by God's inspiration(this includes what he has just written, and the letters/books/epistles written up until this time by the apostles). And we know that in Acts 20:26-28 it is said that the Apostles have already declared the full counsel of God, so for a man to be perfect and thoroughly furnished he must study the already written scripture(by the Apostles and by the OT writers), timothy spoke on this previously in chapter two when he says that a man must study to show himself approved, that he may rightly divide the word of truth(2 Tim 2:15 15
Study to shew thyself approved unto God, a workman that needeth not to be ashamed,
rightly dividing the word of truth.)
Looking at the following chapter we get an even better understanding of what timothy was speaking of when he says that all scripture is inspired by god, and is thus profitable, and also necessary, to bring one to be thoroughly furnished and perfect in the Gospel and in the work of God. Timothy says that we must exhort with all long suffering and doctrine(all doctrine) "
2 timothy 4:2
2 Preach the word; be instant in season, out of season; reprove, rebuke,
exhort with all long suffering and doctrine." He says that we have fully known the Doctrine, and that we must continue in things learned(2 Tim 3:10, 14-15), what doctrine was he speaking of? The doctrine of Christ and the apostles(Acts 2:42, 2 John 9-10,1 Cor 11:1-20), this is the doctrine that was fully made known, the doctrine that was written down and sent out in letters and epistles to each Church just as it was also preached in person. Both the doctrine taught in person and the doctrine taught by epistles were complete and both were the same. If you had one you knew the other, this is why we are told to hold fast to the doctrine taught to us whether by word or by epistle(2 Thess 2:15) since either one was sufficient on its own, and both were being used at the time. Even as far back as Acts 15 we see the Church writing letters detailing the doctrine of Christ and Apostles(though in this chapter it is a very brief letter being sent), this practice continued throughout the lives of the Apostles.
So we see by looking in context and by comparing it to the rest of scripture that timothy was referring to the epistles sent out by the Apostles as well as to the Old testament. But the main point is that timothy was speaking of the Doctrine of Christ and the Apostles.