Why do Russian and Israeli universities score low in various world rankings?
Why do Russian and Israeli universities score low in various world rankings?
  What is the problem? And, why aren't they trying to improve the situation?


As a researcher originally from a country in a similar situation (Austria - historically great, Nobel prize winning researchers - now all universities ranked in the far 3-digit range in most rankings), I can try to speculate. Note that, of course, reasons may differ between Russia and Israel, or between institutions, so there may easily just not be the reason for this phenomenon.


Most rankings are perceived as garbage. Not scoring highly is not perceived as a big deal that needs changing. Unlike in the US and other places, students generally don't care about rankings, and neither do employers. Hence, historically, the universities simply did not care whether they were top-something or not. I think this was the big reason historically in Austria, but it is slowly beginning to change due to top-down pressure from the government. Note that, even today, local students and employers still don't care about rankings, but foreign students and funding sources do, so there is at least some incentive to do something about it.
Most rankings are actually kind of garbage. Many universities outside of the US simply are not as bad as their ranking suggests. Most rankings are either extremely top-heavy in their criteria and hence not very good at distinguishing the 50-best university from the 200-best in a field (e.g., counting Nobel prize winners), or implicitly assume that universities loosely follow the US way of organisation and naming. For instance, my alma mater has historically lost many points in some rankings due to an insanely bad faculty/student ratio. However, this was really mainly due to in Austria only chaired full professors being considered "real" faculty (called "Professorenkollegium"). Hence, the way of counting underestimated the real number of teachers available to students by a factor of 4 or 5. This has, afaik, been fixed by now, but an implicit bias for an US style of organization is still prevalent in many rankings. Further, unlike US universities, there are very little efforts in Austrian universities to tune their numbers for specific rankings. Generally, close to nobody at your average Austrian university has any idea what even the big rankings are looking at.
Being historically good does not mean that the universities are still good. Decades of underfunding for research have severely reduced the quality of research that is being produced. Both things above considered, one has to assert that all the "historically great" universities in Austria aren't actually great anymore. Decades of underfunding, neglect by politicians, and questionable hiring practices for professors have certainly led to big, fundamentally detrimental changes to the university culture. At this point, Austrian universities are still pretty good at teaching students, and there is still reasonable research going on, but it would be wrong to assume that any university actually deserves to be considered on the same (research) tier with top English or US schools. I am pretty sure that at least in Russia, long-lasting underfunding will also be a big reason why the schools don't show up more prominently in rankings.