In a way there are already limits on the distance you can walk. The various methods of delivery have a set time limit and or speed built into planning.
There is also a problem with setting a set distance. The actual distance does not matter but if we take 6 miles in a high density housing area (like back to back council estates for instance) and compare it to a low density leafy suburb, then the estate will get more houses if measured by distance (as now) but the leafy suburbs mail profile means they get heavier volumes and are therefore carrying more weight a longer distance (even if not breaking the weight guidelines).
One of the problems in Deliveries is that Royal Mail seems have fixed parameters in everything they do and don't accept that reality has an effect. If the Union went down that line and had a set distance for delivering on foot eventually you would have people complaining that the limit is unfair because some duties get done up to an hour before another, yet they have the same limit on distance.
Royal Mail cause their own problems because they have fixed attendance call rates for the whole country, rather than by type of delivery (based on density and profile). They also suffer the same problem with failed deliveries for the same reasons.
RM have problems because they plan for an 65 year old to a duty in the same time as an 18 year old.
But RMs main problems are because they plan for 100% efficiency 100% of the time with 100% commitment and 100% accuracy. When in reality nobody, unless they are called Data, can be that good even for a short time.
The Union in my estimation made a mistake accepting BSI for the same reasons. If you are manufacturing a car its easy to time and plan for each component in the process - after all every car gets the same components

and it takes the same amount of time to fit it. In delivering post though, each customer is different, every house is different, every duty is different, every packet is different, and the letters aren't exactly identical either.
BSI - Pick your own definition.
Bull s**t Index
Bosses Shouting Indicator
Bonus Share Increment (for managers)