For starters, EL AL already has the infrastructure for airline ops. They have the people with expertise, the facilities, the routes, the planes (even though id replace many of them), protocols, and their brand image (yes, their brand is worth something even though the company is struggling) etc. Just trying to form a competing airline to replicate the above would take a considerable amount of time and enormous expense.

The above is just a partial answer of why, on a practical level, creating a competing airline as oppose to taking over and/or reconstituting EL AL would be a much more difficult and financially costly endeavor.