Following recent trends neither the mapper nor the vetoing bn can usually reach a consensus on things, mostly either agreeing to disagree or one side giving up. Assuming this proposal goes through, and people still fundamentally disagree with each other, this would end up taking a lot of time and mostly leaving qats in charge of which ways vetoes go, which I doubt is the intended result, as this would lead to vetoes being even more of a pain to deal with for everyone involved except the unvetoing bn.
Currently when a map is vetoed, another bn can check over the map and offer their explanation to why they don't think the concerns are problems, and then have that veto overruled. This means the mapset is both checked completely by both nominating parties and one bn can stop one bn and no more or less.
There are essentially 3 main issues with the current system:
1. The unvetoer needs to check the whole set, whereas the vetoer can simply check one difficulty, which creates an imbalance in effort believed to be unfair.
2. It takes additional effort for the unvetoer to respond to the veto in detail, compared to a non-vetoed map, making vetoed maps less attractive to nominate.
3. Vetoing usually doesn't lead anywhere, often doesn't improve quality significantly and is tedious for everyone involved.
The proposed solution solves the above problems in the following way:
1. The unvetoer can address the concerns that the vetoer brought up without having to check the rest of the mapset, allowing the initial bn to renominate. However, the tables would turn and put most effort on the vetoer, creating the same problem but the other way around.
2. The effort required to respond to a veto is split into two, initial briefly addressing the overall concern of the veto and the second most likely simply being a "I disagree" kind of response, following current trends. The unvetoer won't be able to nominate the map and must wait for a qat to mediate the situation, possibly not even going in the unvetoers favour, even if the unvetoer checked the whole mapset and wants to nominate. This breaks the principle of one bn being able to stop one bn and no more or less, as one won't be able to do anything about what the other did without the qat agreeing to that.
3. Rather than solving this point, the proposal actually makes this problem more of an issue, since it forces the nominators to continue discussing even if a conclusion is already reached, wasting more time for everyone, including a random qat. Only thing this is easier for is the bn who tries to invalidate the vetoing bn's points, meaning mappers might be even more unwilling to discuss things knowing they can get their map renominated if they ask some bn to unveto and it passes.
tl;dr: The proposal makes it easier for mappers to ignore vetoes, should qat lean towards unvetoing (for better or worse), whereas if qat lean towards keeping vetoes, the unvetoing bns won't be able to do anything about the vetoes, even if they checked the whole mapset as they can now.
In my opinion, the current system, even if it still has issues, seems to be better than this one as far as I can tell, but I wouldn't be against trying it to see how it turns out.