> Israel does not actually have legally recognized borders
Let's start from this. Israel has a legally recognized border with Syria which doesn't include the Golan Heights. It also has a legally recognized border with the West Bank on the Green Line, and which doesn't include East Jerusalem. It's that simple. The reason these borders are called "disputed" or unclear, is that Israel refuses to give up illegally annexed territories or- in the case of the West Bank- because the lack of a border allows Israel to keep expanding without officially invading a different country. In other words, the lack of borders is not a bug: it's a feature.
What I expect from Israel as a necessary sign of good will, is to relinquish most of the annexed territories and to declare, once and for all, what are its borders. So that not a single Israeli soldier or citizen could cross them without authorization from the state on the other side of the border.
> They've had several solid opportunities to accept this as reality and establish a state
No they didn't, for the reasons I stated above. In fact, at the present, Israel's government is opposing by all means the possibility of an international recognition of a Palestinian State. Why? Because that would establish a border, and with it the end of Israel's expansion in the West Bank. Since Israel removed a few thousand settlers from Gaza, it has installed hundreds of thousands in the West Bank, creating a de-facto annexation that will be almost impossible to revert.
It also has a legally recognized border with the West Bank on the Green Line.
No, it doesn't. The GP is correct. The "Green Line" is not a legal border. It was a de facto border established along armistice lines between the armies of Israel on one side, and the armies of Egypt, Jordan, Lebanon, and Syria on the other side. https://en.wikipedia.org/wiki/Green_Line_(Israel)
There was also no country called "the West Bank" on the other side of the line. The other side of the western portion of the line in 1949 was Jordan, and it ruled there until 1967 when Israel captured the territory in the Six Day War. Jordan presently makes no claims on the West Bank and agrees its border with Israel runs along the Jordan river.
It has a legally recognized border with Syria.
Again, it doesn't. You are (perhaps unknowingly) once again referring to the Green Line, as per that same Wikipedia link. The border with Syria was a de facto border established by war. To quote Wikipedia:
The 1949 Armistice Agreements were clear (at Arab insistence) that they were not creating permanent borders. The Egyptian–Israeli agreement, for example, stated that "the Armistice Demarcation Line is not to be construed in any sense as a political or territorial boundary, and is delineated without prejudice to rights, claims and positions of either Party to the Armistice as regards ultimate settlement of the Palestine question." Similar provisions are contained in the Armistice Agreements with Jordan and Syria.
Notably the border with Lebanon was the only border in 1949 that didn't include those terms, and was established as the official international borders of the State of Israel and Lebanon. Although Lebanon and Israel have gone to war since, Israel has not tried to annex territory from beyond the Lebanese/Israeli border line agreed to in 1949.
Why? Because that would establish a border
I think your present misconception as to why Israel and the Palestinians have yet to reach peace is due to your misconceptions about borders, since you believe Israel is anti-border in general and that it has repeatedly violated legal borders in the past. The GP is correct that the borders you've claimed Israel has violated were never legal borders, and were merely de facto borders established by war, which both sides agreed were not to be considered valid. When Israel has established treaties that create international borders, such as it did with Lebanon in 1949, Egypt in 1979 (in which Israel returned massive amounts of land, equivalent to larger than the entire remaining state of Israel, in exchange for a peace treaty), and Jordan in 1994, it has not sought to annex territory beyond those borders.
The root issue of the Israeli/Palestinian conflict is... complicated, and a lot more complex than "Israel does not want any borders." One of the core issues that in part torpedoed the Oslo Peace Process is that both relatively-mainstream Israeli Jews and relative-mainstream Palestinian Muslims view an agreement that gives Jerusalem to the other side as a religious heresy that neither is willing to cross, and they both also have refused to share it. But it's not just as simple as that, either. The extreme religious right of Israel (e.g. the Shas political party) views any peace treaty that returns land from the original Jewish kingdom as religious heresy, and the extreme religious right on the Palestinian side (e.g. Hamas) views the entirety of Israel as an Islamic waqf [holy possession] that cannot be owned by any non-Muslim.
Let's start from this. Israel has a legally recognized border with Syria which doesn't include the Golan Heights. It also has a legally recognized border with the West Bank on the Green Line, and which doesn't include East Jerusalem. It's that simple. The reason these borders are called "disputed" or unclear, is that Israel refuses to give up illegally annexed territories or- in the case of the West Bank- because the lack of a border allows Israel to keep expanding without officially invading a different country. In other words, the lack of borders is not a bug: it's a feature.
What I expect from Israel as a necessary sign of good will, is to relinquish most of the annexed territories and to declare, once and for all, what are its borders. So that not a single Israeli soldier or citizen could cross them without authorization from the state on the other side of the border.
> They've had several solid opportunities to accept this as reality and establish a state
No they didn't, for the reasons I stated above. In fact, at the present, Israel's government is opposing by all means the possibility of an international recognition of a Palestinian State. Why? Because that would establish a border, and with it the end of Israel's expansion in the West Bank. Since Israel removed a few thousand settlers from Gaza, it has installed hundreds of thousands in the West Bank, creating a de-facto annexation that will be almost impossible to revert.