The drafting in the bill was actually fairly deliberate. It's put in the negative because these sections, sections 146 to 148, deal with various eventualities or issues that may occur when you're on the list--for example, your name corresponds with another very closely, and that needs to be resolved. It was put in the negative form of “shall not be allowed to vote” so that they have to satisfy those conditions; then they follow the normal process set out in section 143.
Otherwise, if it's put in the positive form of “shall be allowed to vote”, there's the implication that it could mean they are immediately entitled to vote without satisfying other requirements, such as the voter ID requirements in section 143.
That's the reason for it.