On the entire debate of how linked the TTP site are to CBSA systems for passport changes, I can't say, but when I added my Canadian passport to Nexus in 2017 (this was pre the current Trusted Traveler Portal), that update had to be done in person. The US CBP officer took my passport and entered the data, and then handed it to a CBSA officer at the next desk, who did the same thing.

With the new TTP portal, it seems that updates do cascade on existing passports when they are updated (example: you had a Canadian passport on your Nexus profile. You go to the TTP dashboard and update a new passport number and expiration date for said Canadian passport).

The language from CBSA seems to imply that the should be updated at an enrolment center on changes that would potentially impact your eligibility; i.e. a proof of citizenship or a passport from a country that was not previously known. Me getting my proof of Canadian citizenship and then getting a Canadian passport being one such example.

On a separate semi-related tangent, secondary immigration (at least at the level of Immigration 1) does not have direct access to NEXUS systems. When my Canadian work permit got within weeks of expiration, the NEXUS computers started flagging every receipt with IMM-1-1 (go to immigration 1). I'd wait 20-30 minutes in line to get to a CBSA officer at the counter looking at my passport and itinerary info on their computer... who would be puzzled as to why I was referred and said everything looked fine to them and get admitted to Canada with barely any questions. I later found out when I got my passport and went to the YYZ Nexus office to add it that the (then expired) work permit being on my NEXUS profile was an automatic block and they removed that from my profile (the new work permit was irrelevant since I had Canadian citizenship).
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It's not mandatory to have a Canadian passport with NEXUS, there are people that enroll with other documents that are proof of Canadian citizenship and don't have Canadian passport, but chicagoandy likely used their passport not only as a passport but as the identity document that establishes their Canadian citizenship. Also updating a document can be done online (you renew your Canadian passport, input new number and expiration), but adding or removing citizenships or adding/removing passports entirely instead of updating them must be done in person.

I personally would recommend that Canadian/US dual citizens maintain both passports as a Canadian passport proves your right to enter Canada. CBSA does say that US/Canadian duals don't need a Canadian passport to enter Canada but they still highly recommend it so you won't have to carry other proof of Canadian citizenship or go through lengthier immigration screening.

It's a lot easier to maintain the Canadian passport now that they've made occupation based guarantors (if you don't know any Canadian passport holders in the US). Also Kodak moments kiosk software will do Canadian passport photos and validate that they will meet Canada's requirements at any CVS Pharmacy for $17 (+$3 if you want dupes). Also that Canada has (for some time now) offered passports with 10 year validity, instead of the old 5 years... (they still offer 5 years for less money, but between the hassle, the postage, and it being $210 CAD for 5 year vs $260 CAD for 10 year when applying from the US via mail, 10 years is a no brainer.)