In part, because he and other liberals think that the Arab and Iranian (and now Turkish?) war on Israel boils down to an Israel-Palestinian conflict and therefore they over-emphasize this dimension; in part, too, because he subscribes to the liberal illusion that Israel-related issues constitute the "epicenter" of the region (as James L. Jones, then Obama's national security adviser, once put it), so their resolution must precede dealing with other Middle Eastern problems.
But there's another possible reason for Kerry's enthusiasm: he took the measure of Israel's Prime Minister Binyamin Netanyahu and found him indeed serious about reaching an accord with the Palestinians, and not just pretending enthusiasm to please Washington.
This, anyway, is the thesis of David M. Weinberg of Bar-Ilan University writing in Israel Hayom: "Netanyahu has been making uncharacteristically passionate statements about the diplomatic process; statements that go beyond the expected chatter about Israel's desire to engage the Palestinians and negotiate a two-state solution." Weinberg finds Netanyahu "desperate for diplomatic movement[, having] bought into the left-wing argument that the status quo is unsustainable." Weinberg perceives preparations now underway for "a unilateral Israeli initiative to concede significant parts of Judea and Samaria."
Why should Netanyahu, who emphatically did not campaign on this platform, make such plans? Weinberg looks mainly to domestic politics:
Netanyahu has no other national agenda item to sustain his prime ministership. He needs a new message that will reposition him as a leader in the public mind, and the Palestinian issue is all he's got to work with. The lead on economic and social matters has been grabbed by [political competitors Yair] Lapid and [Naftali] Bennett. There's little Netanyahu can do about the hot situation in Syria or Iran. His job is to react wisely and cautiously to developments on these fronts, not lead Israel into confrontation.