But did the road improve because the train service declined? Or did the train service decline because the road improved?
I don't know how passenger numbers have altered, I suspect not that much, but instead of spreading everyone over two coaches of a train, they are now more cosy in one coach. Certainly the London trains have helped ease the situation between Crewe and Stoke (apart from Longport) It is one of those situations where everyone is agreed that longer trains and more trains are needed. It is just none of those feel they should be the ones to pay for it!
The road was improved in the late 90s for a number of reasons - partly to take the strain off the M6 further down by allowing traffic a quicker route to the M1 from the M6 in the Stoke area.
The Derby - Crewe service in its own right doesn't really have great traffic potential - Stoke station only serves a small area of the wider 'Stoke on Trent' area, Crewe is usually a destination to access other, long distance services. Between Stoke and Derby there isn't anywhere significant served.
Do people from Stoke want to go to Derby or vice versa? Probably not.
If you're heading from Stoke you're more likely to head to Manchester, Liverpool or Birmingham, whereas with Derby you're more likely to head for Nottingham, Leicester or Sheffield.
Trying to use this route to 'join the dots' i.e. Liverpool - Nottingham is never going to fly - the contentions for paths at places like Crewe means without a lot of work, its not going to be viable.