It would be interesting to hear from the EU on this (which now exists, skip to the 2nd half of my post for that)... because David Davis thought they would likely reject it:
The Brexit secretary raised concerns that the “facilitated customs arrangement” compromise plan – which would allow the UK to set its own tariffs on goods arriving in the country – was too similar to a discarded idea that the EU had already rejected.
The “third way” customs proposal is intended to end the cabinet clash between the “maximum facilitation” model favoured by Brexiters, which relies on using technology to ensure the correct tariffs are levied on goods crossing the UK border, and May’s once favoured “customs partnership”, which involves the UK collecting tariffs on behalf of the EU.
Davis’s concern is that the EU will block any deal for the UK to police its borders. The Daily Telegraph reported that in his letter he said the plan was doomed because it amounted to a customs partnership with some additional technological elements. The EU has previously rejected both the maximum facilitation and customs partnership models.
But insofar I couldn't find any EU reactions... they were more keen to shake their head at Davis' and Johnson's resignations, apparently. But a response from the EU is unavoidable.
Re: "so why not..." what looks like a workable solution to techie/technocrat may sound horrible to a politician, as shown above.
An analysis from ING concurs:
Will the EU accept the UK’s vision presented on Friday?
Not in its current form - There are three reasons why the EU is likely to reject the UK’s proposal.
Firstly, on the “facilitated customs arrangement”, the EU will likely view this as unworkable
(practical issues of UK collecting potentially higher EU tariffs), legally-challenging (there are
concerns it could encourage smuggling) and politically unacceptable (the thought of a third
country collecting EU tariffs is reportedly unpopular in Brussels).
(The other points for immediate reaction are unrelated to FCA.) The ING analysis goes on to claim that it's likely that the UK will cave in and agree to a full customs union, because the FCA "is halfway there".
Michel Barnier gave an official reply around July 20 basically rejecting the proposal for the (easily anticipated) reasons outlined above:
The British government has said it wants to keep the UK in the EU single market for goods based on a common rulebook. In order to avoid customs checks, the government wants an unprecedented customs system where the UK would collect EU duties, while having the freedom to set different tariffs on goods destined for the British market.
Barnier said this “facilitated customs arrangement” raised practical, legal, economic and budgetary questions.
Setting out the questions he had posed to the new Brexit secretary, Dominic Raab, during their first meeting on Thursday, Barnier said he was concerned that European businesses would face higher administrative costs and there would be increased opportunity for fraud.
Barnier also questioned whether a non-EU country could collect EU customs without being subject to EU oversight. For this reason, EU diplomats say privately that the British plan can never be accepted.
The EU is also deeply concerned that the customs plan would give outsider companies a competitive edge over European rivals if Britain and other countries used the UK as a route to avoid higher EU tariffs.
And in more punditry style:
Michel Barnier said the UK wanted to "take back control" of its money, law and borders - but so did the EU.
"The EU cannot and the EU will not delegate the application of its customs policy and rules and VAT and excises duty collection to a non-member who would not be subject to the EU's governance structures," he said.
Any customs arrangement or union "must respect this principle", he said.