Most people seem to consider all the costs associated with cars as zero except petrol, and for their time spent driving to be considered as zero cost and therefore the value of being able to either be productive or relax on a rail journey is deemed to have a value of zero.
While such attitudes persist, the car will be deemed the winner by most people, most of the time.
Indeed, and therein lies the problem.
To understand that very problem we first have to acknowledge that - whether it be through absolute genuine necessity or simply perceived "necessity" (eg driven by lifestyle choices, or the belief that little Jimmy wouldn't be safe walking to school, or whatever) - a large proportion of us think that we "need" daily, easy, access to a car. And it will be genuinely the case in a proportion: those whose daily commute isn't possible otherwise; those who carry equipment; and so on. And all points in between this and simple convenience. Indeed, even for those who do find train travel more appealing (eg for work while onboard) a good proportion of them will still need to find their way to a (possibly quite distant) train station - most probably by car.
Once we acknowledge this, then it becomes obvious that the car will exist; it will be paid for (or being paid for); it will be taxed and insured; it will depreciate; and it will be serviced and tested - whether or not is is used for any one specific trip. With those things already accounted for regardless, the "cost" of making any one such trip is therefore limited to marginal costs - fuel (most immediately) plus wear on tyres and other components, and (only in more extreme cases) increased depreciation and more frequent servicing. Thus most or all of these are effectively sunk costs.
Second - in many cases (and I'm thinking perhaps more specifically about leisure travel here) any public transport offering is likely to be less attractive (other than to "enthusiasts"). It leaves when it wants to leave, not when the user wants to leave; it may involve protracted waits en route, may well not be direct, will in almost all circumstances take much longer, may well be uncomfortable and/or cramped, and so on.
And third - one does not pay for fuel per use. This is a psychologcal effect only. Set out with a full tank and this trip is free at the point of use. There is a disconnect between paying for the trip and making the trip itself.
So the question becomes - given the above - who EVER chooses to pay a premium for an inferior product? The cost premium isn't that large, on average, for a solo traveller. It may even be negative. But once you become a couple then (notwithstanding railcards, duo offers and so on) the premium increases hugely.
From here to Scarborough (a leisure trip I might make) is around 100 miles each way. It takes about 2 hours by car - and, yes, I do know alternate routes to avoid congestion at busy times, and I do know where I can park for free). 5 gallons at £6 = £30 fuel cost. Double that to allow for other marginal costs (probably generous) = £60. Go when I want; come back when I want; no pre-booking. Change my mind if the weather looks bad and go somewhere else instead; and so on. Best flexible train fare (without discount) just shy of £40 with a trip time well in excess of 3 hours plus any wait time (for the departure schedule at each end), plus 1 hour walking (or another £8 for 4x bus fares) to get to and from the station at this end. As long as I come back the same day. Or £50 if I don't. Double those fares for a couple and there is no longer any contest on price.
From here to Mablethorpe (ditto); forget it. No rail service. Which brings me right back around to already having use of a car.