Jerusalem was divided, but it was not functional for the Jews, as all the of the holy sites were inaccessible to them. The division might be necessary, but not along the 1967 lines.
Regarding “no roots”, it is way off base. For instance, the Palestinians today are the majority of the Jordanian population.
Prior to the rise of Zionism and eruption of the Jewish-Arab conflict, Palestine was not a separate geo-political entity. In fact, the whole Middle East, including the present day Jordan, Syria, Lebanon and Israel/Palestine was a continuous geo-political space, with people freely moving around it. In fact, by 1947, when the partition resolution was accepted, most of the Arab Palestinian inhabitants were migrants from the neighboring areas (Lebanon, Egypt, Jordan, Syria). So, the modern day Palestinians have very deep roots in the neighboring countries. Not that I share the view that those countries should contribute territory.