I agree with Becca.
Perhaps it worked for us only because it was a relationship that we more or less fell into. At the time we had never heard of poly. It was simply that a friend of ours (who had been a very dear and close friend for 8 years at that point) actually wanted a friends-with-benefits relationship because she did not want a relationship that would make any demands that conflicted with her work. She had also had a series of bad relationships which she needed to heal from, so didn't want the complication of an emotional romantic entanglement. The veto was her suggestion, because she was anxious not to stress our mutual friendship. It did work very well for all of us, for about 5 years, until she met someone with whom she was ready to have a romantic relationship. We are all still friends, of course.
I do think it worked very well precisely *because* she really and truly wanted a less-involved relationship: it was certainly a very easy and comfortable introduction into poly for us all. I'm sure I would have been fine even without the veto (especially since the whole thing was my idea in the first place) but I guess it did add a layer of security to what could have been rather threatening. Then again, perhaps not: in fairness, I was never threatened by that relationship at all: we had been close friends for years and I trusted her implicitly to never deliberately do anything that would hurt me, any more than I would deliberately do anything that would hurt her. (Occasional accidental hurt is to be expected in any relationship.) I would also have been fine with the relationship developing into something more romantic if things had gone that way, but they didn't, and nor did any of us particularly hope or expect it to. We were all very happy with the friendship; it was just about meeting other needs, in friendship and love.
The biggest problem that I see with beginning a relationship of a FWB or secondary type (where everybody involved *wants* that relationship structure, of course) is that you simply can't assume that the relationship will remain on that basis. People may start out not deeply emotionally involved, and can believe that things will continue that way, but then find that they have become more serious about one another. At this point, veto power is clearly unacceptable, but it is precisely at this point that the person with veto power may start to feel threatened and seek to impose it.
If people are going to have veto power over their partner's (or partners') other relationships, then it is important that new partners get to meet and spend time with the veto holders as soon as even a hint of mutual attraction is recognised. If a veto is going to be imposed, it should be before people get romantically involved. Once that has happened, you really can't ethically impose a veto. As ever, rules beget more rules, in an effort to be fair to everybody.
A woman on another poly board a few years ago was heartbroken because her partner broke up with her *after 2 years!* because his wife chose that moment to impose her veto. He was unhappy about breaking up with her, but he did it anyway. And the most hurtful thing for her was that it was not by his choice - not because anything was wrong between them - that he broke up with her, but because someone outside their relationship had final say in whether it lasted or not, regardless of how they felt about one another. It can't have done his relationship with his wife much good either, unless he actually didn't care for his girlfriend as much as she thought he did.
Addressing your point, Steady, that only newbies are 'for' veto power. I think it's probably true to say that only the newbies who are already in existing relationships are in favour of it. Except for people in my friend's position - people whose priority is not to harm an existing friendship, *and* who are not romantically involved anyway - I think it's likely that most single people who want to build poly relationships would dislike the idea of the stability of their relationship/s being at the whim of a metamour.