We could but appraising every road in the country seems like a lot of work. And having no default means you'd need to put up millions more speed signs.
You'd have to do that anyway.
The difference is that defaulting to 20 is safer overall.
Why not default to 15 then? 10? Getting out and walking?
I take your point, I do. But it's a simplistic answer. It'd be ignored en masse, just like the 30 limits largely are now; it's a bigger problem which requires a bigger solution than just replacing one arbitrary number with another one.
The problem IMHO in this country is we suffer from 'the boy who cried wolf'. Limits are inconsistent, too high in places, too low in others. Therefore, many drivers (rightly or wrongly) treat them as advisory. If they were more appropriate generally then the great unwashed would take them more seriously.
I saw this in action recently, on holiday in France. Limits are actually lower overall than here, but they are much better at letting drivers make progress when it's safe to do so and then slowing them down again when it's not, that almost everyone drives at the speed limit or close to it. At 70mph in the UK you're constantly either overtaking or being overtaken; at 110kph in France everyone's moving at pretty much the same pace (and lane discipline is SO MUCH better).
Our "intelligent motorways" are a massive step in the right direction; drop the limits when there's a problem, raise it when there isn't. The system demonstrably works. But a blanket dropping of urban speed limits will make precisely no difference until we've got SPECS cameras everywhere, or satellite monitoring. Which is probably only a matter of time.