But it's like car drivers and pollution, right? Cyclists don't contribute any pollution and they don't pay any fuel duty. Land Rovers produce a lot and they pay a lot of fuel duty. Prius drivers produce a lot of less polution and they pay a lot less fuel duty by dint of the fact that they don't need to buy as much petrol to go the same distance. You pay alcohol duty, yeah, but no where near as much as the guys that end up in A&E, because they're not enjoying the odd cider or glass of Chateux-neuf, they've buying 8 jager bombs and 7 pints of piss. The comparisons breaks down, I admit, because the Prius driver does still produce externalities in proportion to it's fuel use (And therefore payment of duty) where as you don't (probably - maybe you Hulk out after 2 bottles of Westons and kick in a bus stop) and yet still pay the relatively less alcohol duty, but hey ho.
I mean, this is true to a point, but not quite. Regardless of the amount you use, more petrols is bad. If I use 20 litres of petrol spread out as 1 litre per day for 20 days, that's equally as bad as if I use 20 litres all in one day, then do no driving at all for the next 19 days. However, if I have 14 units alcohol in a week spread out as 2 units per day for that week, that's far, far less harmful than having 14 units of alcohol in one day and none for the next 6 (probably because I'd be catatonic). In that sense, alcohol is not directly comparable to petrol, because it's not inherently bad, it's bad only in excess.
It's also, philosophically I think, not really any different to charging people for the police time they take up - but it makes no sense to limit that to alcohol. After all, the implication is that everything that's illegal is both harmful and costly (for the prosecution if nothing else), so why not charge everyone? Alcohol related crimes such as the aforementioned bus-stop-smashing is easily more justifiable to me than someone going to the hospital (because of the greater externalities) because they had one too many WKDs, but what about if they punch someone? What if they are on drugs rather than alcohol? And what if they aren't? Afterall, you said "Charging people who end up in A&E for alcohol-related issues is a much more direct link between abuse of alcohol and the costs of that abuse", so clearly you think that making this link is a good thing. This probably sounds a bit hostile which it isn't meant to be, I'm genuinely curious as to where you'd draw the line and why.
Zaph's response is basically how I'd have responded to this. My post earlier wasn't saying "this is a great idea, let's do it!", it was simply a response to "people already pay alcohol duty, so this is unfair". My view is that alcohol duty has no discernible impact on drinking, and this is born out by various studies in the past that show little to no correlation between duty increases and binge-drinking decreases - so people aren't paying alcohol duty because of binge-drinking, they're paying it because the government wants money. Purely from a "people should be held accountable" perspective, the fine is fairer than the duty in that it targets people abusing alcohol more accurately than the duty does.
However, that's purely philosophical, and it's just a shit idea practically, because it discourages people from seeking medical attention, creates an expensive appeals process, probably is statistically likely to punish the poorest, puts an extra burden on NHS staff, and all sorts of other practical implications. I feel the same way about it as I do means-tested winter fuel allowance - philosophically, I think it's absolutely wrong that we give the already wealthy even more, but then the costs of adjudicating borderline cases and the implications for people who accidentally get missed are just too big. It's not practical to carry out the principle.