The as-the-crow-flies distance is not much longer than the lengths of the platforms at New Street. I think the problem is more the lack of a clear, direct-line, traffic-free, walking route. I imagine building one would easily be the cheapest solution. Even a de-luxe fancy elevated covered route with escalators for most of its length would probably work out cheaper than any solution that involved re-routing trains
Another issue is it depends on how useful an interchange would be, and on how frequent the trains are (more frequent making interchange more attractive).
As an example, you could theoretically build a station in Canterbury where the two lines cross, enabling interchange. But the trouble is, what interchanges would you enable? Apart from Faversham-Ashford, almost the only significant journeys that the interchange would allow can already be made much more easily on direct trains that avoid Canterbury altogether. If you kept the two existing stations open, it would also theoretically allow people from either station to go anywhere by changing at the interchange - but the train frequencies at Canterbury aren't really sufficient to make that an attractive proposition.
On the other hand, if you did the same thing at Farnborough or Warrington, you'd make quite a big difference to connectivity, enabling quite a lot of journeys between medium-sized towns that are currently difficult to make by rail.
It's funny that you should mention Ashford to Faversham as it's a journey I've actually done by train (walking across Canterbury). I agree it's not a massive traffic generator, and certainly from Canterbury and Maidstone you have a very good service in all directions.
Warrington is a very long walk between the stations, but you wouldn't want to lose the convenient location of Central. Bank Quay less so perhaps.