Israel's brain drain is serious but it is also one of its life-lines. Whether it appreciates this or not. The constant stream of people traveling between Israel and the West is one of the things that maintain Israel's ties to the US and Europe.
As everywhere in the world the dominant language of discourse in science and engineering is English, and US universities continue to dominate the lists of best and most influential institutions of learning.
If you look around at MIT you will note that 50%-60% of the PhD. students are from abroad. And when they get their degree, they see all kinds of attractive job opportunities right where they live. From start-ups to established companies. And yes, it's one of the ways in which the US attracts talent. It out-competes almost everyone else by offering top-notch education, top-notch research, and top-notch jobs. And that isn't about to change (barring short-sighted politics such as de-funding research).
But perhaps the most important of all: the US really does offer anyone a chance to earn their way solely on personal merit. And that's something very precious that's not available in many other countries where "who you know" counts for more than "what you know".
So yes, there is a tremendous pull. But before you bemoan the big bad US of A luring away all the talent, please realize that there is also (in the case of Israel) a substantial push.
Good friends of mine made Aliyah to Israel about 30 years ago. They were well-educated (an economist and a psychologist) learned Hebrew, did their Miluim (military service), one as a private the other as an officer, and found careers in Tel-Aviv.
What they saw around 15 years ago was a country that increasingly transformed itself from a Western country to a Middle Eastern country. Political polarization, rise of religious ultra-orthodoxy, privileges for religious people (e.g. Torah students exempt from the same military service that takes about a month per year from others), .
What they also saw was a country that was basically unwilling to reach a sustainable accommodation with the Palestinians despite the demographic, economic, legal, and humanitarian issues. They felt the consequences of that in person when their reserve army duties took them to e.g. the Gaza strip where they, in army uniform and armed, would have to face off against 16-18 year old Palestinian protestors / rioters and wield batons (or worse) against people who had no education to speak of, almost no wealth, no opportunities or prospects worth mentioning, no realistic way out, and no serious hopes for improvement. If that were a transitional phase, it would be bearable, but was it? It didn't look that way and it still doesn't.
Attempts to persuade the political majority to reach a sustainable settlement did not succeed (if there were any easy and simple solutions they would have been embraced long ago) and indeed a sustainable settlement seemed drifting further away all the time with the (in part religiously motivated) Eretz Israel (Big Israel) idea.
So they were left with the prospect of staying in an intransigent, polarizing and increasingly besieged country where their children would face the same difficulties, only worse, and without the frictionless alternative of having a double passport.
So they decided to leave and they are not alone. Obviously that segment of the population with the most portable assets (intellect) has the best prospects of leaving.
That's the "push" part of the equation.
So, yes, there's brain-drain but a lively exchange of people and ideas is (as I see it) needed for Israel's mental health. Also there are reasons for the brain-drain that have little to do with big bad US gobbling up all the talent.