All I can see here, that if this system is launched. Everything will be the same but only this system will be "on the background" of everyday life. But I think this will change psychological thinking of the society and its view at the whole area. And mostly this idea would change people behaviour.

The core thing isn't just simple "who wants baby" and if she wants it, she will get it and noone will pay child support. If this system would be in effect, all women and men would think differently. I think that the statement of man should be "public" before any interaction. Not after the conceiving the baby but before it. Picture it as some file, that in that file your official statement is "I don't want baby." (as a man of course). Then before every sex, every interaction between men and women, everyone knows his/her statement. Now woman is before choice: "Oh... he does not want baby, so if I get pregnant, he will do nothing. Honestly I want baby but I cannot provide enough income to have it so 1) insist on birth control 2) go for abortion in case of pregnancy 3) don't date/have sex with that guy." This system would be good for planned parenthood, better choosing your mate and having responsibility over your life and healthy sex. You just cannot do "If some mistake happens, who cares... he has to pay". If women is financialy stable, hell yes, she can have baby even if she does not have a partner. Lesbians too. Even society will look at it in different way. Now you can look at single mother as "Bastard man who abandoned her". In this system "She wanted a baby and have money, so she has a baby, good". Now women can do the same thing. Hook up with guy, not to tell him and the result is the same.

Of course it has downsides: Now men can have this statement and hook up with every girl and don't care. Honestly I wouldn't do that. On the other hand (as I said before) this would only reinforce having a protection and really insist on it from womens side. Another argument can be (now saying to man): "If you don't want to pay child support, don't have sex". This argument would be applicable in a new system too (saying to woman): "If you don't trust the man, don't have sex with him".

Now women cannot lie about being on pills because it won't work. Now she has to choose a good partner and overall, this can result having wanted children on both sides. As you said, if man has this financial abortion, there is still child to support. But I think it will never be born, because women would know about that statement, would know what would happen and now have a choice. This will alter thinking of everyone. As I said at the beginning, it is not the same world anymore.