I, too, cringe when I read anywhere that Kate is wearing Diana's tiara. I think basically its because most people can and do identify the Lover's Knot tiara with Diana as she wore it so beautifully. Now it seems to be on a lifetime loan to Kate as it was for her mother-in-law.
As for the sentimentality of Kate wearing it, no one can really know but I would imagine that it warms William's heart to see the woman he loves wearing something that he remembers the other woman he loved so much wearing. I believe that William, himself, is sentimental about this. Back in 2010 when William and Kate became engaged, he said this about the engagement ring. "[Kate's engagement ring is] my mother's engagement ring, so I thought it was quite nice because obviously, she's not going to be around to share any of the fun and excitement of it all — this was my way of keeping her close to it all."