I'll offer a recent experience in Spain, to alert people to the dangers of removing "Break of Journey". Having travelled in France on local trains, stopping off here and there (on the same day), I then purchased a ticket from Port Bou to Barcelona, thinking that the same would apply in Spain. The idea was to stop for lunch and continue onward.
The station chosen for the lunch break had unmanned barriers. My attempt to pass through with a ticket to Barcelona (further along the line) was rejected. I managed to attract the attention of the clerk in the ticket office, who agreed to let me through the barriers but telling me it was not permitted. He told me that he was going off duty but he would inform the next employee to let me back in. When I returned after lunch, once again my ticket did not open the barrier. The new clerk behind the window in the ticket office told me that I could not enter but must buy a new ticket from there to Barcelona. Luckily the distance and cost from there to Barcelona was small. She told me that she was not allowed to let me through the barrier with my Barcelona ticket.
If Break of Journey rights are removed in the UK that will likely bring to an end starting or ending short, having a break for lunch etc. and catching a later train, walking between stations and so on. A single ticket of any kind will simply be point to point. They'll call it "simplification of the rules". The time validity can be restricted also, so that once a ticket is purchased the journey must be completed for example within two hours.
Be careful what you wish for.