@rfeng Thanks to you and the community for responding. I did do some research regarding your question and it seems like the steps you took are the only native way to delete the frequently called list. However, upon my research I did find an app that might help you. The link below will be able to take you to the market site where you can get information on the app. I hope this helps. Thanks.
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Tried Clearmaster...........doesn't work. I've tried several different apps and they don't work. Clears everything else but that.
Must be particular to Galaxy Nexus.
I've put it out there on Google to see if someone comes back with a positive response. I'm still not sure how to forward a product enhancement to Google though.
I believe that the quandary I am coming into is that I am almost at the end of my opportunity to switch to a different phone. Due to the fact I need to have more direct control over my phone and what it does I can't completely say that the Galaxy Nexus is footing the bill.
There are things I like about it and if the issues I presented were tended to..........I'd stick with it. but it's pushing me into a corner where I won't be able to say anything that positive about it. I'm trying to avoid that by seeing if I can get someone to provide the solutions and lay all of this to rest.