First of all, I agree that the current situation is unsustainable, and until 7.10 I was out in the massive pro-democracy protests in Israel wearing a T-shirt that read 'There can be no democracy with occupation'. Like most of the Israeli left I think that the end of the occupation and the establishment of a Palestinian state alongside Israel is vital for the security and prosperity of both Palestinians and Israelis.
However, from your question I think you misunderstand about the current situation. Within the state of Israel there is no ethnic segregation. Palestinian Arabs (about 2 million people, who make up 21% of Israel's citizens), hold Israeli passports, vote, serve as members of parliament and senior members of the judiciary. All religions are entitled to freedom of worship, days off on their religious holidays etc. Could there be greater equality? Yes of course, and many of us on the Israeli left are doing what we can to make that happen (and the current far right government is not helping). Look up organizations like Standing Together, the New Israel Fund, the Abraham Fund, Hand In Hand schools, just to name a few off the top of my head.
The issue you are talking about is the situation of Palestinians in the West Bank and Gaza. This is not segregation within a state based on ethic origin/religion, it's military occupation as the outcome of the continuing failure to implement the two state solution, and to understand it and solve it it's important to know the background.
Until the end of WWI historic Palestine was part of the Ottoman Empire. After the Ottoman Empire collapsed, historic Palestine was administered by the British as the British Mandate for Palestine. There was increased Jewish immigration in this period due both to Jewish national aspirations (which were supported by the British) and to Jews fleeing from the Nazis, and there were tension between Jews and Arabs. In 1947 the UN resolved to end the British mandate and create 2 states in historic Palestine, one Jewish and one Arab. The Jewish leadership accepted and declared the State of Israel. The Arab side did not accept and the Arab countries waged war intending to eliminate the state of Israel. This didn't happen, rather Israel won the war with some terretorial gains, and the Palestinians suffered the Nakba (catastrophe) where large numbers were expelled by Israeli forces/left voluntarily/were encouraged to leave by the Arab forces and many others were internally displaced.
At the end of the 1948 war, the West Bank was under Jordanian control and the Gaza Strip was ruled by Egypt. This was the case until 1967. In the Six-Day War in 1967, when Israel once again fought the Arab armies. You can read about that separately but the upshot was that Israel ended up occupying the Gaza Strip and West Bank. This is still the situation now. There have been numerous attempts to establish a Palestinian state in Gaza and the West Bank via peace processes (Oslo Accords, Camp David, etc etc) but those were not successful with each side blaming the other for their failure. In 2005 Israel withdrew unilaterally from the Gaza Strip but Israel and Egypt still control the borders of Gaza. The West Bank is still under military occupation.
Why not turn it all into one democratic state? It sounds good on paper but see my answer two questions ago - it's not what the 2 peoples want, both want independence, and those calling for one state generally actually want one state which is THEIR state, not a utopian binational entity. The only viable stable solution to this national conflict is 2 states as originally envisioned by the UN, and this is still the official position of the PA , Israel and the international community (even if on the ground many politicians don't always act/talk that way). But the challenge is not in understanding what should happen, it's in actually implementing the solution, for which strong politicians who have the mandate to make compromises have to be found on both sides. Aside from compromises in territory and natural resources, the two state solution requires Palestinians (and the Arab world) to accept the existence of the State of Israel and to give up the goal of "freeing" historic Palestine from the river to the sea, and it requires Israelis to give up most of the West Bank settlements (some might remain with land swaps) and to trust that Israel can be secure next to an independent Palestinian state. For the last 20 years or so, both sides have not been willing to make these compromises.
On the latter point, unfortunately the experience with Gaza has made Israelis even more hesitant about security, as Israelis look at the situation in Gaza: Israel left Gaza in 2005, a year later Gazans elected Hamas, and since then Hamas has been waging every kind of battle to scupper the 2-state solution or normalisation between Israel and Arab states, most spectacularly on 7.10 which occurred just as Israel was moving to normalise relations with Saudi Arabia. In order to end the occupation Israel would need assurances that a similar situation wouldn't happen in the West Bank. That's where the international community would have a big role to play in the transition. My one hope coming out of the current war would be that all sides would understand that we need to move seriously towards a two state solution as both sides are losing hugely from the current impasse.