I can see the benefit on routes where there are a lot of advanced tickets, to help passengers get on the right departure.
The problem is the large number of "non-standard" services that we have. For example, there's a lot of services that we think of as regular hourly routes. But over the course of the day, these don't all have the same stopping patterns.
Take the longest Cross Country corridor. Generally Edinburgh to Plymouth, with around half the services starting at Glasgow (but some services to/from Aberdeen/ Dundee/ Penzance etc). Would all services on that route have the same number? In which case, how do you deal with services that stop at Berwick/ Alnmouth/ Burton/ Tamworth? Would the Aberdeen services have the same route number as the Glasgow services? Including the one that runs non-stop through Dunfermline (avoiding the regular Kirkcaldy stop) for route learning purposes?
If my regular bus into town is the 37 then I can be pretty confident what stops its going to serve. But a train service can vary from one departure to the next. Taking the Harrogate example above, at the moment there are services from Leeds that terminate at Harrogate/ Knaresborough/ York... some of which run fast to Harrogate, some of which serve local stations (there can be six/ two/ one intermediate station between Leeds and Harrogate). Should these all have the same route number? Or do you need three numbers for most Northern services (fast to Harrogate, slow to Knaresborough, slow to York) plus a different number for LNER (which don't stop at Hornbeam Park)?
I'm not trying to sound awkward - it's just that if you "simplify" things then they need to be properly simple. Someone who boards a regular "37" at Leeds station to their home station should be confident that an earlier/later departure branded as "37" will serve the same stations.
I think it'd work fine on simple corridors like Merseyrail, where almost everything stops at every station (two "numbers' required for Chester services, given the fast/slow versions) but I think that you'd generally need to have simpler timetables without as many deviations. Which then begs the question of whether it's worth either having *every* Edinburgh - Plymouth service stopping at Burton or *no* Edinburgh - Plymouth stopping at Burton, for the sake of a simpler route diagram.
I can see arguments both ways, but you need to consider the everyday passenger who would rely on the route number to identify a service from A to B (and potentially find themselves on one of the services per day that runs directly from A to C, omitting B)