There are those who also believe the woman represents the Church. The problem with your view, however, is that Israel did not bear witness to Jesus as the Son of God. Remember that the Apocalypse (or Book of Revelation) is apocalyptic literature unique to the first century. Thus, it is full of symbolism which has multiple meanings. Therefore, it is common for one symbol to represent more than one thing. The woman clothed with the sun is the Virgin Mary, and so the verse should be principally interpreted as such. This is demonstrated by Rev. 12:17, where the devil goes to make war on the rest of her offspring, on those who bear testimony to Jesus. This makes Mary the mother of all Christians.
Since Mary is the mother of the Church, we can say that the woman, on a secondary level, represents the Church, which is the New Israel. This is why John writes about her pangs of travail, which are symbolic for those who are being formed in the Church of Jesus Christ. So, this literature provides us multiple meanings, but there is generally a principal meaning and a secondary meaning; in this case, the woman is the Blessed Virgin Mary, the same "woman" who God said would crush the head of the serpent in Gen. 3:15. Because she is such a danger to satan, satan tried to kill her even after the Savior was born (Rev. 12:13).
Great explanation.