Are you seriously trying to suggest that it doesn't matter if people who need to use peak trains (and would have been willing to pay high fares to get on them too) can't board the trains? Seriously?
Let's turn this around, if it's such a great idea, should we do the same thing for road travel?
I'm sure there's quite a few people who would be willing to pay to drive their cars on much quieter roads.
I disagree: It will influence people's thinking in ways that would be economically damaging.
Again, we have free to use roads and the economic costs of congestion (see for example the case of the economic harm which is caused each time Operation Stack is implemented).
In this scenario, living further away carries the benefit to the commuter of a nicer house. It also has two disbenefits: To the commuter of the longer commute and an external disbenefit to everyone else of the increased pollution plus resources used.
There are already quite a few people doing some very long commutes. The fact that there's congestion would impact people's behaviour. However, you only need to see the impact of house prices as you get further from London to see that people do apply a significant value to their time.
As I said, increased population is unlikely to be as impact as you make out:
- if a train is running anyway the extra energy required to be carrying 500 people over 200 people isn't that large
- you wouldn't need many of those extra people to switch from cars (and even fewer from flying) to wipe out those extra energy requirements
- you wouldn't need many people to not buy a car to offset the resources to build an extra coach (in part due to the fact that train is likely to make it 35, whilst cars typically only make it to 17)
Best resource use/economic efficiency is achieved if the commuter chooses the nicer house ONLY if all benefits outweigh all disbenefits. A sensible pricing system for the railways, in which the fare roughly covers the external costs, will achieve that: The commuter will choose the nicer house if she/he feels the niceness outweighs the longer commuting time plus higher fares (which represent the external disbenefits).
Sorry to keep bringing it up, but again the provision of free roads would have a far larger negative impact than free rail.
On the other hand, if rail travel is free, the commuter will likely choose to travel further if the niceness outweighs the longer commuting time alone, without taking into consideration the external disbenefits. So they may well choose to commute longer even if the total disbenefits outweigh the total benefits.
(And as a side note, that's an example of how providing stuff for free will in general cause economically inefficient decisions that ultimately make us all worse off.)
Although charging for stuff also brings about a lot of economic inefficiencies too.