Earlier quoted context omitted.
It's quite strange to me that people would identify as or look for a "[language] programmer". Sure, I happen to write more C++, Python, and C than anything else, but I've dabbled in just about everything and could reach comfortable proficiency in a matter of weeks. Most of programming and all of computer science is universal. Any serious programmer should be a polyglot by default.
This is why Joel Spolsky correctly observed that the replacement of C/C++ and functional languages with Java in university CS curricula is a tragedy. If you don't understand pointers or recursion, you are not a polyglot and you cannot pick up just any language in a matter of weeks. The "[language] programmer" (where [language] usually = Java or .NET) trend is a misguided attempt by industry to commoditize programmer…
C/C++ programmers tend to do premature optimization (habit) due to the culture and the problem domain (past experience): device driver, kernel code, game development.
How important Pointer is for say learning any high-level programming language that don't have pointers (pretty much everything outside C/C++/Objective-C)?
Sometimes I felt that knowing Pointer arithmetic and tricks are some sort of chess-thumping that old programmers tend to do. (My background is system programming so I know how pointer works).
It doesn't matter what you know or learn during the university. What matters is whether you continue to hone your skill or not and have a high bar of quality.