Really they are providing different products but giving incentives for people to take their product over competitor's products. If LM applied to run a Birmingham-Euston direct express service then I doubt ORR would approve the application even if there was a path available to do so.
Northern Rail run a Manchester-Stoke stopper but you can't really say they compete with XC and Virgin for passengers travelling between Manchester and Stoke as they offer an inferior product (slower service with commuter style interior) and no incentive to use the inferior product like cheaper tickets. LM and Chiltern offer the cheap fares to get passengers to use their 'economy' service over a competitor's 'premium' service.
As I was coming into New St on Monday I saw a huge Chiltern bill board saying "Are you still a Virgin?", on the board it was proclaiming how Chiltern was just as comfortable as Virgin services for half the price. Virgin and Chiltern not competing..... Come on pull the other one. Chiltern have pumped huge amounts of money into their line as they have a long enough franchise to make the investment worth it. Would the same investment have happened under BR? I doubt it.