Wisdom of the crowd also implies that diversity of human bias is a good thing, in aggregate.
To more closely address your point: if all companies use the same LLM they’ll all have the same hiring bias. But if Company Foo has Hiring Manager Bob that’s biased against me, I can shoot my shot with Company Bar with Hiring Manager Alice who might not be.
In practice I doubt many people are aware of their biases either, or think "it's not bias if it's true" or something. But at least on the less "internally" biased end of humans there will be less external manifestation of it.
If you talk to 100 instances of chatgpt during 100 separate interviews you'll have 1 single bias source
For instance, if I discuss audio electronics with Google Gemini, depending on what kinds of questions I ask, I can get audiophile crackpot quackery out of it, or I can get solid electronic engineering statements.
The training data contains a vast number of narratives that are filled with different points of view. Generally speaking, you get the ones that resonate with your own narrative threaded through your prompts.
One way is if you ask loaded questions: questions which assume that some statements hold true, and are seeking clarification within that context. If the AI hasn't been system-prompted or fine tuned to push back on that topic, it may just take those assumptions at face value, and then produce token predictions out of narratives which express similar assumptions.