For most proposals, the writer is often not connected to the research that prompted the proposal. For example, I wrote two proposals this year, one on storm-petrels and one on swamphens. I have not written about either subject otherwise and have no stake on the outcome. For some proposals, the writer recommends a no vote. And for almost all proposals , the work is already published and the writer's stake in the Committee outcome is rather small. For academics (including most members of the SACC and NACC), it is much more important for job security, raises, tenure and such to get papers published. The administrators and colleagues that decide our fates usually have little or no idea what these Committees even do and could not care less whether one of our proposals passes through the Committee.
Anyway, I think the Committee works best when it makes it informed decisions. If the proposal is written by someone who is involved in the research, then they are likely the most informed and I value their opinion. As it takes a super-majority for proposals to pass, the vanity of one Committee members is not going to outweigh the sanity of the rest of the Committee. For all these reasons, I see no reason to bar votes from those involved in the research or proposal writing.
Since you like drawing analogies, in the US congress, a bill sponsor (often the writer) may still vote on their proposal. Not sure what they do in the UK parliament.
Andy