I like your analysis, however there is a conflation of three types of third party custody.

Bailment is when you permit a third-party custody of your keys, for example if you pay for a 'backup service' of your wallet keys. Something like keys.casa is an example of this. This is a bailment relationship; the property is bailment, you are the bailor and casa is the bailee. You are entrusting your property, your bitcoin wallet, with a third party but they don't have any use-rights or title over your property while its in their custody. When you leave your keys in bailment, you would expect the third party should not move your funds around or use your wallet as they see fit. With bitcoin, you would have evidence of this misuse on the blockchain, and if you noticed anything changing in your wallet, you would reasonably be concerned. This is a case where the bailee is holding a non-fungible good in their custody, that is your wallet address and not the bitcoin itself.

Bitcoin keys are a special type of property. it is intangible and it is a secret. Once your secret key has been disclosed to the bailee, the information can't be 'removed from custody' with absolute certainty. You would only have a guarantee from them, which requires residual trust that they have removed all records of your secret. With bitcoin, it makes sense for the bailor, rather, to simply move the funds to a new wallet rather than extending this trust. In the case of physical (tangible) property its much simpler because once you reclaim posession of a physical thing, there is no remaining potential right by the bailee. Saylor has a very good article on this

In the case of a crypto/fiat exchange, your funds are co-mingled into bitcoin wallets of which you do not have the private keys to. This is called tenancy in common, where the exchange is presumed to be solvent at all times and your funds are always available for withdrawal. In effect, you have a demand deposit with a non-banking entity that is holding your fungible good and you have common tenancy in that exchange's wallet with all the other clients of the exchange. We all hope the exchanges are solvent and 100% reserve, though I doubt many will offer a public audit trail to that effect.

The bank enjoys the best of both worlds of tenancy in common yet with title; this due to a court decision legalizing fractional reserve for demand deposits. In England, a 1832 court decided that an implicit contract exists between a bank and a depositor (A loan in mutuum), and this allows banks to redefine a depositor's ledger not as a deposit of a fungible good with tenancy in common, but instead involves transfer of title from the individual to the bank, and the depositor now is a lender to the bank redeemable upon demand. The legal penumbral trapezium used to justify this decision involved conflating a bailment with tenancy in common, where the argument before the court was whether a demand deposit was a bailment over a particular set of coins on deposit and not whether it was a tenancy in common over a fungible good. This permitted banks to operate on fractional reserve, and obtain rights over the funds they otherwise would not title to lend out.

Does this get you started?