We all know that if El Al treats its business partners half as badly as it does its business customers, there's no chance of them joining an alliance.
Star Alliance has a huge number of overlapping partners, we know that's not the issue.
El Al likely negotiated too hard, and is too inflexible, by nature of it being an Israeli company. They need to accept fair terms and join an alliance for the benefit of their customers.
One of the many reasons I avoid El Al - outside of Tel Aviv, your status is worthless.