A contact these days is more than just a name and a phone number or an email. It has an address, notes, organization name, notes and much more...
Why cant I search a contact by just how I remember a contact. e.g. I sometimes remember people by their organization or by where they live, and I know I have stored that info in my contacts. If mobile phones (e.g. iPhone) can index all your emails and let you search that, why not index everything in a contact and search by anything or everything.
e.g. I wanted to find out a contact, and I knew the phone number started with area code (916). Why cant I just start typing 916... in my contact search, and it starts shortlisting people.
Again, simple, but still missing.