Educational self sufficiency
According to the OECD: Israel's spending per-student is low relative to other OECD countries. Given that countries like the US have both higher spending per-student and higher enrolment rates, it is not clear what a switch to heavier state subsidisation (both the UK and US already heavily subsidise universities) would achieve. Bear in mind that most of the best US universities privately subsidise talented students from poor backgrounds so that the highest fees are mostly bourne by the wealthy.

It seems that implicit in your question is the idea that Israel rations its heavily subsidised tertiary education by imposing more demanding entrance requirements, but it is not clear to me that this is true. The entrance requirements for elite universities such as Harvard, MIT, Oxford, or Cambridge are among the most demanding in the world. There are 4599 higher education institutions in the US that cater to a very broad spectrum of student types.