I think these are good points, making one person a mentor can make them a bottleneck. I think a team of people responsible for on-boarding is a very good idea. However, that has the pitfall of not having an actual ‘owner’ for the new-hire — as in — who is the point person he can turn to? Edmond Lau, author of The Effective Engineer outlines some good ideas in his book and blogpost http://www.theeffectiveengineer.com/blog/how-to-build-a-good-onboarding-process-for-new-hires-at-a-startup
What is important is for the entire team to understand why a good on-boarding is in their best interest. Having a very strong contributor is important in order for the larger team to become high functioning. This needs to be internalized by everyone. Only then can they actually figure out the importance of a good on-boarding process and become active participants there.
I think having good internal literature in the form of codelabs is crucial to create a process whereby there isn’t a lot of repetitive activity happening. Additionally, what is also important, exactly as you said, there needs to be time dedicated to inculcating in the new-hire the values and aspirations of the company and their team. The product sidekick is a crucial to allow the engineer to really understand why the problem they are working on is important. Even there I would suggest that it not be just one person, different members from different parts of the organization should be talking about how/why they work on what they work on. But at a more team level yes I agree that a product sidekick is supremely important.