You don't see them doing that because they already did it very thoroughly decades ago. Maybe you didn't hear? In 1948, as soon as there was an existing Israel that promised to accept all Jews... all the Arab nations expelled all their Jews, most of whose families had been there for more than a thousand years.
It's only since the 1970's, and the wave of Russian and American immigrants, that Israeli Jews are majority Ashkenazi -- before that they were mostly Mizrahi.
You don't see them doing that because they already did it very thoroughly decades ago. Maybe you didn't hear? In 1948, as soon as there was an existing Israel that promised to accept all Jews... all the Arab nations expelled all their Jews, most of whose families had been there for more than a thousand years.
It's only since the 1970's, and the wave of Russian and American immigrants, that Israeli Jews are majority Ashkenazi -- before that they were mostly Mizrahi.