One is a semi-reformed terrorist organization that is looking for legitimacy, the other is a right-wing government that probably doesn't give a fukk about the Palestinian people at all, but can be pressured to back down because it has not staked out such obstinate positions. Better yet, they have a government that has shown that it will negotiate peace in the past.
I think you're displaying some unwarranted assumptions here yourself. The current administration won't be persuaded to give the Palestinians any kind of
practical political sovereignty. Their idea of a 2-state solution would leave the Arabs with completely permeable borders that are dominated by Israel, almost no economically-viable land that would support an economy, etc. I think that's an empirical point, too, when you consider the details of their ideas in previous negotiations. Just because this administration (thankfully) doesn't run with the genocidal desires of the extreme Israeli Right, doesn't mean their plan will produce anything fair for the Arabs.
You're really trying very hard to disavow logic to support your sympathy for Palestinian plight. So you're telling Israel to call Hamas' bluff and meet them at the table (mind you I'm completely against them settlements), and have what to show to their people? "Yeah, they haven't acknowledged our right to exist, but we're hoping that they'll be on their best behavior."
Think about this from a power perspective. The Arabs quite literally have almost none, so there's no legitimate reason for Israel to fear anything new going in. That being said, the negotations wouldn't be with Hamas, especially if they're UN-brokered. Hamas governs the Gaza Strip, which is only one of the Palestinian territories. The PLO (which has relatively minor Hamas representation in it) and maybe the PA would be the ones on the opposite end of the table if Israel wanted to talk. In addition, even if negotiations started now, there's no telling which administrations they would end with, so it's not as if Hamas (or Likud) will be the two defining intermediaries of the general political will on either side.
Your right that from a Likud perspective, there isn't much reason for them to negotiate beyond the distant end of the conflict, but that mentality itself is only going to be an obstacle. Asking the Palestinians to shape up before they can come to the table is less reasonable than asking Israel to for a number of reasons, imo.