I can't know what Biden is thinking. However, the Palestinian situation is different than the Hezbollah/Iran situation. I think as a general rule, people don't want to see the middle east explode. But it seems neither side is giving the other much choice.

I tend to agree with you here. Since the attack was launched from Iran, it is appropriate to target Iranian weapons production, military assets, and command and control (including leadership). Missiles would be best since Iran is not a neighbor, and it would require flying over non-combatant nations' airspace to get to Iran. Israel sending fighters invite them to be shot down, which would expand the war. Iran already set the precedent launching missiles through Jordanian airspace.

I know Iran generally doesn't like their theocracy, but it would be a mistake to think they would welcome Israel like the Parisians welcomed US soldiers in 1944. There probably won't be many roses. At best, if the Israelis can weaken the hold of the theocracy, maybe the Iranian citizenry could take it from there.