I’m wondering whether something like this might happen…

Step 1, cut off liquidity to unregulated exchanges.

Step 2, allow people to buy BTC via their banks.

Step 3, require all personal wallets to be registered (by giving the IRS your xpub), or alternatively to have all BTC transferred to a registered custodian.

Step 4, disallow transfers of BTC to unregistered wallets.

Step 5, disallow receipt of BTC from an unregistered wallet.

If there were sufficient penalties for noncompliance, most people would likely comply and the banks can force their way back into the middle, at least for people in the US.