Map reduce and filter often are much more readable, but then sometimes a loop is clearer. I often see this when I use resharper's (a c# tool) auto refactor a loop into a linq statement , it can become unreadable.
Readability depends on both the underlying algorithm and its expression in code. Because LINQ has to work in existing languages, it can't express loopless algorithms as well as languages like J that have syntax designed to fit the style. You're probably also putting it at a disadvantage with the automatic translation, as you'll write different and cleaner array code if you approach the problem with array operations in mind.
The author is claiming (and I and many more practical-minded programmers agree) that in J, explicit loops are rarely needed, and usually not even helpful. As the J notation is designed for loopless programming, it has the same kind of bias, against loops. But knowing how J approaches things can be valuable. Most likely, many problems you think are unapproachable with map and reduce can be solved easily by knowing the right techniques.
Plus they may have hidden performance costs - or benefits. They may have function invocation and memory layout costs, but they may also be parallelised and optimized transparently. A regular for-loop is super efficient in terms of memory layout / access but it's by definition singlethreaded.
Yes, as always, it depends. The typical problem with array operations, e.g. in Fortran, is how well they're "scalarized", and the possible cost of not doing copy elimination over subroutine calls, for instance.
Presumably the exact semantics of a for-type loop depends on the language, but surely the C standard doesn't prevent auto-parallelization (including with SIMD vectorization, modulo arithmetic rules). Loops might also have OpenMP or other annotation.
The author is claiming (and I and many more practical-minded programmers agree) that in J, explicit loops are rarely needed, and usually not even helpful. As the J notation is designed for loopless programming, it has the same kind of bias, against loops. But knowing how J approaches things can be valuable. Most likely, many problems you think are unapproachable with map and reduce can be solved easily by knowing the right techniques.