Originally Posted by televisor

1. The GE application asks you to disclose all citizenships. IIRC submitting the application means that you're confirming that all the data enclosed is correct and complete, which it isn't if you've not disclosed all your citizenships.
(The reality is that they usually don't care, but technically you're giving them a false declaration by not stating all citizenships.)
2. There are other people here who have multiple citizenships, none of which are US, and at least one of which makes them eligible for GE. As a foreigner using GE you want to be pretty damn sure your application was correct. And it might still be useful to have more than one passport in the system for such people (e.g. possibly me in the future).

Also: there are definitely cases where CBP very much do care about second citizenships. Just look at the stories of ESTA for dual EU+Iran/Iraq/Sudan/Syria citizens (for citizens who might not even be aware of said second citizenship).