Please note that I didn't say that the barrier could just be removed.
Indeed among both the Israelis and Palestinians, there's a small percentage violent men (mostly men), for example, a small fraction of the people in IDF shot a thousand people in Gaza some years ago (about 100 died, don't remember exactly).
And a small fraction of the Palestinian men in Gaza fire rockets against civilians (although they pretend they target military but they don't) and I think eventually some people like them would blow bombs if they could get past the barrier. And that would restart a circle of violence, bad for everyone.
> How else do you propose they quell the proliferation of arms
That might take about a generation.
Examples: Stop doing bad things to one's neighbor: Don't send soldiers with weapons to the West Bank, building settlements and taking other people's land, forcing them to leave. You can websearch for "Breaking the silence IDF" maybe combined with "male soldier Gaza" or "female border police" to find out other things individuals in IDF or the border police sometimes do, that can create and keep alive such hatred you mention. (And maybe is that kind of hatred, just this time from some Israelis against Palestinians.)
And do kind things to one's neighbor: Share the Covid-19 vaccine with the Palestinians: Reverse time and give it to high risk group in Palestine, instead of first to low risk groups in Israel. Support women in Palestine who start their own businesses -- women are generally more peaceful and the more influence they have, the better.
And about the barriers: More buses, more checkpoints, and more staff in each checkpoint, so takes less time to pass the checkpoints. To respect other people's time.
There're probably 100s of things to stop doing, and 1 000s of things one could start doing, to create peace and friendship. Then, continue like that, for one (maybe two) generations, and it'll be fine.
(Plus doing kind things to the people in nearby Arab countries, so it'll be harder for dictators or corrupted politicians there, to say bad things about Israel -- which they apparently do a bit much, maybe to divert attention from problems in their own countries. For example, share the covid vaccine with the people in Lebanon.)
However I think Netanyahu and Hamas or Jihad group leaders, need conflict, to get more votes and stay in power. Isn't Netanyahu popular partly because many voters think he's saving them from danger. Too many of the voters don't realize that he is part of creating the danger. And the same goes for Hamas and jihad groups. And they'll want to continue taking land, and firing rockets, doing the opposite to what I mentioned above.