It depends on the job. Some jobs it's not relevant, other jobs it is. For a general purpose programmer, the more they understand the better.

Sure, a library for the common problems already exists, but if you can't provide a reasonable stab at the standard stuff yourself, then you have no chance of solving the unique problems that you may run across. Also, if you're familiar with the algorithms used for standard operations: reverse, random shuffle, sort, that kind of thing, then you will recognise when aspects of your problem already have solutions.

You may as well ague there's no point teaching kids to add and subtract by themselves because they can use a calculator.