That is an option. I think it would be important if we want really consistent estimates documents, and by that I mean those reports one, two and three, and we want the appropriation bills to be consistent with those documents. Then, yes, we need to bring those two together.
I think it's possible, but it would be a huge shock to our public servants to actually run the two processes parallel behind the scenes. I think we use this veil of secrecy perhaps too strongly, saying that we need to keep people out of it. The budget is typically produced by people at the Department of Finance and the Privy Council Office. A lot of the treasury people are a step behind.
It is possible for this to work collaboratively behind the scenes.