IMO, the reasons for algorithm testing are the following, but not limited to:

Unbiased assessment of candidates for "apples to apples" comparisons

See if the candidate has skills deeper than typical day-today skills that can called on if needed

Demonstrate an understanding of performance trade-offs that have profound economic impact on the delivered solution(s)

Demonstrate the ability to create solutions beyond "textbook" solutions when required

Screen out quickly candidates who lie about their technical capabilities on their resume

I hope the above list is useful and/or helpful.