On the matter of free travel, perhaps a distinction needs to be drawn between the accompanied and unaccompanied of the species. Whilst I agree that, in the same way as I did at that age, kids going on social leisure trips should contribute towards the cost of providing the service. But, for example, a family of four making a journey would have two adults already paying their fares which, in itself, would exceed the equivalent cost of travelling by car. To charge children in these circumstances may make public transport a very cost-ineffective option, and would do nothing to encourage those children into a public transport mindset.
When my kids were under 14, I had a Family Railcard which in those days charged a flat fare of £1.00 per child. Suffice to say that if I had to have paid a half fare back then, even at the railcard discounted rate, Shell and Esso would have would have got a lot more money out of me than British Rail would have done...
It is always an unwise move to base opinions on ability to pay on the resale value of domestic property. For example, my mother and stepfather bought a farm cottage on the Gloucestershire/Herefordshire border that they were previously renting in 1970 for £2000. He worked as a farm labourer/ hedge layer/ JCB driver all his life and never earned enough to pay higher rate tax. He is still there, now widowed and not in the best of health. At a rough guess the old man lives in a place worth about £750,000.
Will you tell him he’s too asset rich for a free TV licence? I won’t – he’s a cantankerous old bugger at the best of times...
In terms of a difference between accompanied and unaccompanied travel, I agree that it would be appropriate to make a distinction. The family railcard discounts feel an appropriate balance. As an example, off peak fares from Bristol to London are:-
1A : 63.10
1A, 1C: 53.65
1A, 2C: 65.65
So effectively, with one child the cost is lower, two children can travel for free, and any additional adults go for a third off too.
As for the position of your father, I don't think public policy should be based on how cantakerous people are likely to be. Those who live in a property worth a lot of money are able to release some equity through various equity release schemes if they so wish. Whilst I would caution against using these too early or for than a modest share of the property (say 50k in your example), they are a way of rebalancing one's assets to meet living costs. Many people use these schemes to fund their new kitchens, cruises, new cars, etc, (probably to an extent which is ill advised in my opinion), so why not for other purposes?
It all comes down to whether society wishes to subsidise those who have assets, albeit illiquid, at the cost of others in higher taxation. If you explain to less well off young people in the north of England that they have to pay more tax because society is funding care costs to those with property worth hundreds of thousands or even millions in the south east, so that those assets can be handed to the next generation of already middle aged high net worth people, I suspect there would be some discomfort. Unfortunately the argument is never put like that.
It's not only the super-rich either. In my own position, when my father died about 5 years ago at 95 he left a relatively modest house (less than £200k) in Newport. To look at him he was a poor pensioner, and didn't spend much. But he lived comfortably on his pension, balancing his income and expenditure, and didn't need a free tv licence, winter fuel allowance, or free bus travel to do so. Had he had to pay for those, our inheritance might have been £20k lower split between the three children. So has the state got good value out of those vital non means tested benefits he received? Not in my opinion.