Does Carreyrou give reasons for eliminating Hal Finney from being (part or all of) Satoshi?
Yes, he mentions he was photographed running a foot race during a date and time Satoshi sent emails (of course that's a bit weak).
If you believe that Satoshi's email wasn't hacked then his last emails came after Finney had passed away.
The reporting already establishes all three parties (Satoshi being the third) were familiar/friendly with one another. The reporting says that Finney was the recipient of the first ever Bitcoin transaction, which seems like a completely natural thing to do if the two of you are working together.
Finney's name also rises to the top in a few of the author's analysis, while also noting:
Again, why not both of them as Satoshi?Hal Finney's passing also helps explain how such a monumental secret of Satoshi's identity has remained a secret for so long. The only other person who's in on the secret is Back himself.
Edit: To add further conjecture, it wouldn't surprise me if Satoshi's wallet is locked away in a trust or tied up with Finney's estate. I can imagine a scenario where the keys to the wallet are legally unobtainable until such time that both Finney and Back have passed, at which point the wallet is liquidated and its proceeds donated (Finney previously raised money for ALS research).