Good point, but also a rather tricky one. One could also regard a tax on petrol as a pollution levy (currently, it's not used as such either), and on that basis ask "what should a litre of petrol cost when we include socio-ecologic impacts" (or in other words, what is the 'true price' of petrol, including life cycle costs'. This question inherently borders on policy, but I'll try to avoid that angle (my preemptive apologies if I do cross the line somewhere).
The question is notoriously hard to answer - there are short-term impact in terms of health (dust/respiratory), direct environmental damages (oil leaks, general landscape damage due to mining), and the long term impacts due to CO2. For all, probably estimates have been made, but I am most aware of the latter.
The estimates vary widely, from a ~$50/ton to several thousands of dollars per ton. A recent estimate based on a macro-economic analysis, using the most likely IPCC scenario with a retuned version of Nordhaus' DICE model, comes to ca. $420/ton CO2. As burning 1 liter of petrol emits ca. 3 kg of CO2, the CO2 cost alone would be 3 x 0.42 = 1.26$/litre (using this model). And most likely, this approach is under-estimating: the DICE model assumes the macro-economic impact of local temperature is a smooth function (not accounting for tipping points), and if I'm not mistaken, a linear function. That's all rather unlikely; when the temperature gets close to the point where sweating can't cool a human body anymore, economic activity will be impaired much more severely. And that limit is more and more frequently hit in parts of the middle-east and south-(east) Asia.
Now, as mentioned estimating the cost itself is notoriously hard (as it comes with future predictions on migration, crop impacts, etc. due to climate changes), and adding to that, the number is dependent on our action (as responses will be non-linear in reality). Still, having an estimate of these costs and including them in the petrol price (instead of 'blind' taxation) is essential. By including those costs, the polluter pays for their pollution. By not including them, the costs of pollution are put upon society as a whole (and disproportionally those in countries that added little to the pollution). And in case society pays, the bill only comes when the damage is already done - when the polluter pays, it is pre-emptive, and can be used to mitigate damages, by subsidising alternatives, as you mention, or otherwise. (oops, policy alert)
Also, without such a 'true price', economic comparisons between BEVs and petrol vehicles don't make much sense, as a large part of the real economic impact is omitted. Claims that 'BEVs can only compete with subsidy' generally forget that petrol vehicles are also effectively subsidised currently. Naturally, the requirement to allocate true costs goes both ways - BEVs also have their external costs that need to be accounted for.