I think Israeli strategy (such as it was) in 2006 was to tip the party's cost-benefit analysis, in the hope that the Lebanese population would exert pressure on Hizballah to cease activities that brought Israeli retaliation —-or, otherwise, risk increasing alienation from its popular base.

This worked quite well in the 1970s against the PLO, which went from immensely popular to immensely unpopular in Lebanon. However, Hizballah is an indigenous actor with great reservoirs of goodwill in the Shiite community, and Israeli actions were in any case poorly calibrated to achieve this effect. When Israel started bombing gas stations or bridges in northern Lebanon, for example, many Lebanese bought into Hizballah's position that this was a preplanned Israeli war of aggression, and that Hizballah was once more defending the country as the "national resistance."

I suspect a sustained and extensive ground operation would have backfired in similar ways, and would have likely ended with Israel withdrawing under fire (again).