The Bible speaks for itself ... so you ban teachers from teaching their preferred doctrine and stick to just what it says
The Bible is a book, not a person.
If it speaks for itself, then it hasn't spoken very clearly, since there manifestly is widespread disagreement as to what it says.
Even if we stipulate that your premise is unproblematic, it is impossible for teachers or anyone else to refrain from comment on something as important as Scripture. Even the tone of voice in which it is read will convey much information about the reader's estimation.
The fact that in this case the passages read will be carefully prescreened by a government agency indicates that bias is already at work.
The Bible is not intended to be a tool of worldly policy.
This is the big lie put about by the "Sola Scriptura" clique. There are a myriad of opinions on what certain passages from Scripture mean. What you mean is that when you read the Bible, its meaning appears obvious and it speaks for itself. It also speaks for itself to the guy who just opened up a new storefront church in the local strip mall.
However, his views on certain passages of Scripture are not the same as yours, despite the fact that you both agree that the Bible speaks for itself and that Sola Scriptura is the only way to go.
Scripture itself, says that certain parts are not easy to understand.
And account the longsuffering of our Lord, salvation; as also our most dear brother Paul, according to the wisdom given him, hath written to you. As also in all his epistles, speaking in them of these things; in which are certain things hard to be understood, which the unlearned and unstable wrest, as they do also the other scriptures, to their own destruction.
2Peter 3: 15-17