Hi, thanks for all the replies! yeah Will and Jesse have got it. My issue is not with blend, but rather with sweep and revolve using 'joined' lines. Evidently joining two lines doesn't create a single segment curve, since the surfaces resulting from sweep and revolve have split lines. Blending or filleting the two edges so they are tangent before joining also doesn't solve the problem.

So the last point made by Jesse has it in a nutshell. Only by going over the line again with a 'through points' curve to make a single-segment curve can you make a non-split surface when using it in a sweep/revolve. But this seems a bit bizarre, surely there must be a better way to do it! As Michael says, the "deleting the point at the join" method will change the shape of the curve, but is a valid solution.
Anyway, the .3dm file I attach is a trivial example of a sweep and revolve using joined lines, which demonstrates this issue. I wouldn't bother looking at it really, nothing exciting!

You seem to be able to separate the joined lines afterwards, which indicates that the 'join' process is not quite what I thought it might be. Maybe you could keep join the way it is, but if the lines are tangent at the join it could ask you something like: "merge tangent lines?" which would mean an extra click is not always required.... but the more I think of it the less convinced I am by this! I'm really glad you're keeping the UI clean and well thought out Michael, it really shows.

Thanks for the suggestions everyone!