The Charedi adage that the state of Israel was founded to destroy Judaism, as the Brisker Rav said, is true but myopic. It’s not just Israel! All states are founded so as to destroy all religions (especially by co-opting them).
Firstly, the authorities of each are mutually exclusive. Either God rules men or man rules men.
As Leibowitz recounts his conversation with Ben Gurion:
Some twenty years ago I had a lengthy conversation with Ben-Gurion, whose attitude toward Judaism is well known to you, about the problem of religion and state. He said to me: “I understand very well why you demand the separation of religion from the state. You want the Jewish religion to be reinstated as an independent factor with which the political authority will have to contend. Therefore I shall never agree to the separation of state and religion. I want the state to hold religion under its control.” The official representatives of Jewish religion are resigned to this state of affairs; even worse, they count on being “kept” by the secular government.
Secondly, they cannot lastingly abide family guardianship or self-government or private education, either.
The interests and memories which spring from local customs contain a germ of resistance which is so distasteful to authority that it hastens to uproot it. Authority finds private individuals easier game; its enormous weight can flatten them out effortlessly as if they were so much sand.
Even false opposition to the state like Cursedianity is too scary.
Intentions aside, the results have been mixed.