Not saying I agree, but I believe the general argument is that if tax was already paid/collected when the fuel was purchased, unbundling it from the fare price prevents it being taxed again.

How are fully-consumed process inputs handled in VAT? It's easy to calculate non-consumed inputs. They paid $x per kg of aluminum. Each finished product contains y kg. So the "cost basis" for each product is $x * y.

But what happens to, say, the electricity used to melt the aluminum before being poured into molds?

I think it works as follows: say you make sales for one million plus 20% VAT. You get paid 1.2mn, but 200k are for the taxman. However, you already paid VAT for your inputs, say 30k for 150k in materials and 20k for 100k in electricity. You then give to the state only 150k: the 200k you collected minus the 50k you paid (i.e 20% of the 'Value added' 1mn-150k-100k).

Ah, that makes sense. Relatively easy to calculate compared to the itemization I was thinking of -- at least, I'm assuming it can be aggregated in a way that makes the calculations easy.

VAT only taxes added value. So, if VAT applied to fuel, the airline gets a VAT rebate for everything that they buy (including fuel), and then pays VAT on their total sales. Nothing is taxed twice.

If there's some tax benefit to splitting a fuel surcharge out, obviously taxes on fuel aren't an ordinary VAT...

Fuel duty is its own thing in Britain, so at a complete guess maybe fuel duty subsumes/replaces VAT but then companies aren't able to offset it like they can with VAT?