I believe that Israel has gamed the invasion of Lebanon ad nauseum, and for decades it has planned securing the land south of the Litani River.
The last time Israel tried that in 2006 they were driven out by Hezbollah and Hezbollah has gotten much stronger in the interim. And if Hezbollah enters the war it’s also likely that other state actors in the region enter the war against Israel. The US can only do so much to assist Israel with the limited military assets we have in the region.
Israel is taking a huge gamble risking a regional spread of this war, seems like they are going for broke. Personally I think they are seriously underestimating the military strength of their enemies and overestimating the assistance the US can provide for them. I stand by my earlier prediction that a regional war would mark the beginning of the end for Israel.