I mostly agree, but would add two caveats.

Relying too much on getting one very specific advisor is risky. Most advisors are middle-aged (or outright old), especially those with Nobel Prizes, and they do sometimes die or move away with little notice. If that happens, universities can be very bad about finding replacements (let alone comparably brilliant replacements) for any students cast adrift.

Also, an adviser's personality & schedule are as important as their research skills: a Nobel Prize winner who's usually away giving speeches, and is a raging, neglectful arsehole when they are around, is likely to be more of a hindrance than a help in getting a PhD. Put like that, what I just wrote is obvious, but I can imagine it being the kind of thing potential applicants would overlook.