On top of the other issues discussed, I think that giving effective oral exams is hard for the same reasons that interviewing is hard. It’s a test of the subject’s ability to quickly and confidently say things that sound roughly correct. Some people stumble over their words and cannot effectively speak and think completely accurately in the time required to give a reasonable answer without an uncomfortable pause.
Now, these issues could be mitigated by asking each person the exact same questions and taking careful notes of their responses, but then you’re just back to a bad essay that can’t be revised, edited, planned, or recollected as easily as a real essay.
Exams can be anonymized when graded to reduce teacher bias. You can't do that with oral exams. In addition, you can't get a second opinion for an oral exam if you suspect you've been graded unfairly.
Language ability, manner of speaking, physical stature and presentation, reputation from previous interactions with staff, you name it—all worsened by the fact that many of these are probably going to be done by course staff. It's not clear to me that any other form of assessment has as much potential for subconscious bias.
Orchestras started using privacy screens for auditions for a reason. And I'm not familiar with an equivalent for the human voice, particularly for hiding halting, labored, or elliptical speech—possibly by a non-native speaker—that they could straighten out on the page.
But then why say "equity"? Blind grading can, of course, eliminate bias and achieve equality. But to achieve equity, you need to know the race, sex, religion, etc in order to "positively" discriminate.
That being said, the ultra dense morons who think "oral" can't be extended in a special case to simply mean "without extra time to think" (which is what is is, mostly) are typically not experienced with these exams.
The parent teaches CS1 and is not likely to have been given a formal oral examination in their likely short career (these are usually reserved for PhD qualifying and special MScs).
Now, these issues could be mitigated by asking each person the exact same questions and taking careful notes of their responses, but then you’re just back to a bad essay that can’t be revised, edited, planned, or recollected as easily as a real essay.