The big reason is that the F-22’s main weapons bay was designed for AIM-120 AMRAAMs under a “not a pound for air to ground” philosophy.
So it can only hold air to ground weapons up to 1000lb class.
The F-35’s weapons bays are designed for weapons up to 2000lb class, which includes a family of penetrator/bunker buster guided bombs.
Since Israel would be expected to rely on a stealthy aircraft for deep strike, decapitation missions against hardened targets, the F-35 is the only choice right now that fulfills those mission requirements.