No, this is largely propaganda.
There is a resolution in the UN right now, has been since 1998, that lays out a path to peace. All it requires of Israel is that they obey international law, including returning to the 1967 borders. 138 countries in favour, two abstentions, and, you guessed it, the United States and Israel voting against.
This resolution has been voted on several times over the years, always with overwhelming international support, and with Israel, the U.S., and occasionally one or two other countries voting against.
Just for clarity's sake though, no, Palestine isn't just Gaza and the West Bank. And you obviously can't have a Palestinian state that isn't contiguous. The driving of Palestinians from their homes didn't stop at the Nakba. It's continued up until today, with Israeli settlers stealing land in the West Bank right now, using October 7th as a pretext. If you're not aware of what the Israeli settlers are up to, you should spend a little time researching.
Sure, 1948 wasn't yesterday, but neither is it ancient history. People alive today remember the Nakba. They remember their parents being killed and/or displaced even though they'd done nothing wrong and had been living in those homes for generations. This wasn't "reckless," it was absolutely wrong and shameful. And asking them to just "draw a line" under it is insane. They're going to remain angry, as any human being, including you, would be under the circumstances.
Of course, if there's ever going to be peace, they're going to have to accept a compromise. I'm not suggesting that the Israelis living there now should simply go back to wherever their families came from (although I'm curious whether your magnanimous philosophy on immigration applies to all immigration). But as I said, there's a compromise on the table that Palestine have already agreed to and that has near-unanimous international support. The stumbling block there is Israel and the U.S.