Or… they could just leave them as they are and display both, and therefore people can use whatever works best for them?
I have no objection to both being on the sign, e.g:
Southbound Victoria Line
towards Brixton via Victoria
Disagree, much easier to learn how to say (well, read) compass directions in a foreign language than to have to work out what the terminal stations of each line are, and locate them on a big confusing map.
The problem is that the lines are sort-of staggered through central London, so the compass directions aren't always obvious, unless you simplified it (which it doesn't) and considered that Victoria, Jubilee*, Piccadilly and Northern were always run north-south, Central always east-west, "Wimbleware"** north-south, the rest of the District and H&C east-west and the Circle clockwise/anticlockwise.
But your issue is why I'd also include a key Zone 1 via point, which is very likely to be where they're going or at least somewhere they've heard of. For the Victoria Line in Zone 1 these would probably be "towards Brixton via Victoria" southbound and "towards Walthamstow Central via Kings Cross/St Pancras" northbound.
* The U shape is indeed confusing.
** I jest slightly, but I do wonder if that bit of the District actually would benefit from its own name and colour.