That may be the case now, but for that to be seriously considered there would need to be a major expansion of capacity, both to meet the increase in demand and to provide services where there are none. Many journeys outside major towns and cities are impractical and often impossible by public transport. For such a policy to get widespread support it would need to provide a far more equitable service across the country, which would cost a lot more.
Which is why further on I assumed an extra £1,000, as that would allow extra capacity as there's already some government cost to providing public transport.
Also, in working out our, one of the factors I used was the total TfL revenue, however as that includes road pricing there's a fair chance I've over estimated the cost. Likewise, looking at First Group's revenue will include some from rail. I did this to provide a robust number, to ensure that I want overselling it.
However, there's likely to be some cost savings/other income too. For example a station with a ticket office and gate line staff could see some reduction in staffing numbers whilst still providing more staff available on platforms. Likewise the ticket office (and queuing) space might be able to be rented out for retail to generate an income.
However there certainly would be cost savings from faster bus journeys (as the loading process would be faster) and a whole load of back office staff (for example those processing refunds, those following up on those caught without a valid ticket, etc.).
I'm not against free public transport (I do think the tax burden on working individuals is way too high but that's another conversation and imo resolvable by shifting the tax burden rather than decreasing it) but I'd be surprised if you tempted too many people out of a second cars from it. You're assuming people have the second car to transport them from location A to location B without any meaningful luggage or time constraints. I don't think that that applies to most people who need (or perceive they need) the second car.
I'm sure there'll be plenty of people who have the mindset that they'll need a second car anyway.
It does of course depend on why they have a second car and one person's experience and observations can be very different to another's.
Someone who is working and needs to do a certain amount of work can either need their journey to be very fast if they can't work whilst travelling (for example driving themselves) or to be able to work efficiently enough to justify a longer journey (for example if the train allows them to do some work if it takes a bit longer that's not an issue).
Likewise, if you need to get a child from school to ask after school club by a given time, it may not be possible to use public transport. However, if that's only once a week, it could be that journey could be done by car (how that is achieved may depend on personal circumstances - for example for some the other parent may work from home that day, for others it might be a car club car, for others car sharing, for others it might be changing the time slot, for others it maybe something else - however that still doesn't mean that for others they still keep that second car).
However, it's surprising just how many people who have access to a car but who have been given a bus pass are willing to use it.
Anyway, often lower taxes doesn't mean lower cost. For example, locally many people pay £50 for garden waste collection. However a fair chunk of that payment is likely to cover the admin in running the scheme (taking the payment, sending reminders about renewals, ensuring the most of houses to be collected from is to to date, etc.). It may well be that if you put up council tax by £50 (above inflation) everyone could have garden waste as well as better other services which they may also have to pay for (either to the council or to a business).
To give an example, in Iceland they pay a flat rate for their energy to the government as apparently it would have cost more to create a billing system than it would cost to provide the energy. Now let's say that's slightly exaggerated and the billing process was going to cost 500 and the energy averages out at 1,000. That would mean that for someone to be worse off they would have to use less than half the average amount of energy before they even started to feel that it would be cheaper for them to pay their share of the billing process as well as their energy costs.
Now that cost may well be down to the fact that there's just under 400,000 people and so there's not significant economies of scale (but then the same could be said of some our smaller country councils and over 270 of the nearly 300 district councils - although they might be able to buy an off the shelf product to to help keep their costs down).