Generally, finding people most similar to someone would be a great service. And if it could adjust for age, you could like start a "community of you" overnight. You'd no longer need to go online to get your echo chamber.
It would be a powerful thing, both for good and bad.
I see a few problems with creating such service. The most boring is the chicken-and-egg problem: the service is most useful if it had data about many people, but how would you convince the people to give it data if it is not useful already? (Potential bootstrap: scrap internet data from blogs and social networks, and proactively send recommendations to some people.) Which data is it going to evaluate? (IQ and the big five?)
When the Dalai Lama dies, I hear they search for a child who is presumed to be his reincarnation.
Whether or not you believe in reincarnation, if a person dies, there is still a child out there who is most similar in personality to the deceased, by some measure. If it was straightforward to find that person, we could hand on to them everything the deceased collected in their life: objects and advice and perhaps even connections with people.
Usually a person’s things are given to their family, who somewhat appreciate it, but often mostly for the financial and sentimental value, rather than because it contains exactly the collection of photographs of birds that they most want.
Relatedly, I feel like it’s taking me ages to figure out how to be a well-functioning person, and if someone very similar to me had already spent a lifetime working it out, it would be great to have that data.