Most people have a car and so the cost comparison should be to compare the rail fare to the tangible cost of driving, which for most will be the fuel and parking (few places have congestion charging). If you own a car, the ownership costs of tax, insurance, MOT and servicing have to be paid no matter how little or often you drive. Delays aren't a tangible cost unless the extra time taken to complete a journey has directly denied you the ability to earn money (how would you honestly have used the time if you weren't delayed?).
For me, to visit family, rail fare around £100 now that advance tickets are virtually unobtainable. Driving, £40 in petrol, and whilst up there, I have the ability to visit a national park, hike up and down a big hill, and get back in time for an evening meal.
Many people use rail because despite its faults, it is the most practical (or only feasible) way to make their journey. I use trains to reduce driving mileage and/or when cycling the distance would render me heavily fatigued, because I try to live more ecologically responsibly. I was fortunate two Sundays ago that bike and train from Horsham to Pyecombe was quicker than cycling the full distance (helped by the train home turning up at Hassocks at the exact time I arrived at the station and short connection times).
It does matter how few miles you travel and/or how much your car costs to run each year.
If it's costing you £3,000/year and you're doing 1,000 miles than it would be cheaper to use a taxi!
However, given that if you've got a car then your do more miles in it then you need to then it could be that the cut off is much higher. For example, those who suggest that they need a car for a supermarket trip (and assuming that they don't want to use internet shopping), for many it's entirely possible to walk/use a bus to the shops and then get a taxi home. In doing so reducing by half the miles traveled.
Likewise a child with swimming lessons after school where you couldn't walk the distance in the time you could walk to school, taxi to the lessons and then walk home. Again reducing the distance traveled.
That's in addition to those trips where the distance is short and the car is used when there's no need to.
That's not just me saying that, but is backed up by data. 1/5 of all trips in London by car are less than 2 miles in length. Now not all of those would be suitable to be undertaken by walking/cycling however the majority probably could be, even if that was one way walking.
Things like internet shopping do require more planning than going to a shop, however they can been done in a lunch break or on a train for delivery at a convenient time. Which can mean that you have more time for other things.
Early on in the internet shopping lifecycle I met a farmer who realised that by getting their shipping delivered that it saved them about 2 hours of their time. Now for them it was a 40 minute trip each way to go to the supermarket, which made a big difference to their time saving calculation, however even fairly small distances can start to add up, especially over a year.
Whilst the first few times it can take a long time to fill your online cart, most people have the same things week after week, so it speeds up after a while.
However it's a task that can be done it what would otherwise be dead time and can be done in small blocks of time too. For instance of you the app on your phone you can add 5-6 owns whilst cooking dinner in the same way as you'd add then to your shopping list.
Likewise a DIY project, unless you run out of the right thing part way through our need just a few little bits, then it's probably easier to get the stuff delivered to you rather than trying to play car Jenga with the various bits. As to running out of bits, the spread of Screwfix has resulted in them covering some fairly small locations, however there's often independent shops who can also mean that for many they're not that far from extra parts of they need them.
