I think the problem is extending the deadlines. Parishes know that they needn't worry about it because the deadlines always get extended. If the government said "your exemption will end in 2024, no exceptions and no extension", every CodE parish will be registered in time for the deadline. I've just checked the requirements to set up a charity and get it registered and they are not onerous. There are certain supporting documents required, but a church parish could just take the equivalent documents for another parish as a template for these. You are required to have your accounts properly audited, which is why my suggested deadline is 2024 and not 2023 - to give time for a full audited financial year to pass, but that is the only even slightly tricky hurdle.
Yes I agree - until the government actually sticks to a deadline then there is no incentive for the churches to do anything to get themselves registered.
And I'd actually go further, doing nothing makes it almost certain that the government will simply extend again, so there is a clear incentive to do nothing.
So as far I can see the CofE has done virtually nothing to register its churches, given that they haven't even bothered to register their largest and most significant churches, namely their cathedrals. So as a deadline approaches their line is effectively 'sorry, I know we were meant to register our excepted church charities, but we haven't got around to it. And there are 35,000 of them so we'd overwhelm the commission'. So the government extends and years later the CofE says, 'sorry, I know we were meant to register our excepted church charities, but we haven't got around to it. And there are 35,000 of them so we'd overwhelm the commission'. And on it goes.
But this is, of course, a choice by the CofE - there is absolutely no requirement for 35,000 churches to be registered - it is entirely in the CofE's discretion to group churches into larger charitable units which are registered as a single charity. The most obvious block being a diocese as there are already organisational and administrative structures that require individual parishes to report to and be controlled under the diocese structure. So this would mean presenting just 44 charities for registration, rather than 35,000. And there is a precedence, in that this is exactly how the catholic church has sorted its charities. But why would the CofE make this choice, when it can just ignore the requirement knowing that it can play its trump card of 'sorry, I know we were meant to register our excepted church charities, but we haven't got around to it. And there are 35,000 of them so we'd overwhelm the commission' every 5-10 years and still retain the special privilege.
So my solution would be that the government and commission should set a non-extendable deadline and also indicate that the commission can only register a specific number of charities per year and it is therefore up to the churches (and specifically the CofE) to work out how to organise its charities registrations to allow the commission to register them, or lose their charitable status. I suspect if the government and commission did this, we rapidly see 44 registration applications coming forward in short time.