This is an important question. However, I'd like to point out that similar biases can easily exist for non-ML, hand-tuned algorithms. Even in the latter case test sets and often even "training" and "validation" sets are used for finding good parameters. Any of these can be a source of bias, as can the ears of evaluators making these decisions.
It's true that bias questions often come up in ML context because fundamentally these algorithms do not work without data, but _all_ algorithms are designed by people, and _many_ can involve data in setting their parameters. Both of which can be sources of bias. ML is more known for it, I believe, because the _inductive_ biases are less than in traditional algorithms, and therefore are more keen to adopt biases present in the dataset.
It's true that bias questions often come up in ML context because fundamentally these algorithms do not work without data, but _all_ algorithms are designed by people, and _many_ can involve data in setting their parameters. Both of which can be sources of bias. ML is more known for it, I believe, because the _inductive_ biases are less than in traditional algorithms, and therefore are more keen to adopt biases present in the dataset.