Because if I need to drive 30 miles to an "inter-city" station and leave my car there, and pay for parking as inevitably there won't be free parking there, I more likely to just drive all the way.
I think this is one of the many negative aspects of multimode travel:
When someone makes a journey they have 3 things to consider: cost, convenience and journey time
If they are less able, or carrying heavy luggage they will prioritise a direct/one mode service over a faster or cheaper multi mode journey or even consider a slower direct train (a good example would be Peterborough - Warrington, faster via London, but not attractive if you are less mobile or have a lot of luggage)
Business travellers probably prioritise journey time over cost
Lesiure travellers may prioritise cost above the others
The problem with switching modes of transport during a journey is that all three considerations take a hit. If you have to drive to a main station (Hull or York in my case) that means less convenient, higher cost (parking at York is an eye watering £17 per day during the week), and the possibility of there being no space on arrival. Buses, where they run, are slow and not designed for people carrying significant luggage. The other problem is that with a few exceptions bus and rail timetables are not integrated. Buses are also still at the mercy of road congestion, bus lanes in cities go some way to address this, but once you leave the cities there is not much you can do.
Having good local as well as inter city rail services ticks the boxes in terms of convenience and journey time. I predict that if you cut the rail network back to the point where most of the feeder branches and local stations are closed then even this rump would be unsustainable within 5 years. An interesting statistic would be the proportion of revenue and journeys that originate or finish using local or branch line services. If these services were removed I would predict that over 75% of this revenue would be lost. To relate an example I gave in an earlier post in this thread, Home > Hull > London KX > Paris, losing the local service would probably tip the balance towards flying, with the route being Home > Leeds-Bradford > Paris CDG > Paris RER, i.e. total loss of revenue to UK rail. This journey, even using advance tickets will cost around £200 return per person. Flying is sometimes cheaper, but currently convenience makes rail more attractive, and journey time is similar, with rail just having the edge door to door (Airport check in times and luggage retrieval at the other end really add up, also strict baggage weight limits).
So unless you have a rail system that offers local travel there will not be a rail system at all as it will wither and die.