UPDATE: This question was the subject of my blog on November 13th of 2012. See it for some more thoughts on this issue. Thanks for the great question!
You’re right; it doesn’t have to be that way. Other OO languages allow “private inheritance”, whereby the fact that D inherits from B can only be taken advantage of by code that has the ability to see B.
This was a design decision of the original C# designers. Unfortunately I am away from my desk right now – I’m taking a couple of days off for the long weekend – so I don’t have the language design notes from 1999 in front of me. If I think of it when I get back I’ll browse them and see if there is a justification for this decision.
My personal opinion is that inheritance should be used to represent “is a kind of” relationships; that is, inheritance should represent the semantics of the domain being modelled in the language. I try to avoid situations where inheritance is used as a code sharing mechanism. As others have mentioned, it’s probably best to prefer composition to inheritance if what you want to represent is “this class shares implementation mechanisms with other classes”.