Well, yeah. Who are these people that you want to silence but don't want to unfollow? What would unfollowing do, which you don't want, which silencing would not do?
From the Smalltalk world, I'm pretty much interested in every single tweet. Besides, people in this group don't tweet that much.
As for musicians and bands, we usually follow each other in order to stay aware of gigs, recordings, etc. But following is also an act of befriending, so there are bands and individuals who tweet way too much but to whom I still want to show interest, so I can't unfollow them.
Friends and acquaintances from my town, however, you've got to follow them... and some of them are really annoying. I don't want to unfollow them because, as OP said, «few of them might get offended and then your relations might ruin or something like that». If you live in a small enough town, you'll know what I mean :)
But as a gesture of politeness, you might want to follow someone who has followed you and is close to you, but at the same time you would not want to listen to all his tweets, in that case, silence might work, and not unfollowing.
That functionality has become indispensable to me, and I hate reading my timeline in other clients.
After all this, I switched back to plain Twitter and built my interest lists (smalltalk, music, friends, etc), but having to visit all these lists all the time became tedious too.
It's been around half a year I haven't read my Twitter timeline at all.
I know it sounds stupid for the way Twitter is meant to be, but until there is a functionality allowing you to silence people you follow, I just can't use it.
I know, why would you follow people if you were not interested in what they tweet? I guess I'm stupid.