Are Block Sizes Still Relevant?

[DavidB]

Looking at several FORTRAN routines, many of them call sub-routines to determine block sizes of a particular problem.
For example, DPOTRF takes in a matrix and a few other parameters, and then passes them into ILAENV, which returns an optimized block size for the problem at hand and the hardware running the code.

I am wondering, is this consideration still relevant with today's hardware and software?

Say I am using a C-like translation (C, C++, Java, JavaScript, etc.) on a standard desktop computer.
Does calling ILAENV provide any benefit to the program in terms of accuracy or speed of execution?
Would the program perform the same if I just explicitly assigned a block size of, say, 16 (or some other integer)?

Any advice?