Understand that I have no data to support my opinions... but here are my reasons for keeping a few no fee cards around indefinitely, in declining order of importance:

(1) There is a FICO element for "length of credit history" which is determined by the single oldest account. I'd like that number to continue aging as I do, so I keep a few accounts open in case one gets shut down for whatever reason.
(2) There is still the 10-year time horizon to consider. If I have a few no fee cards around growing into the decades of age, it adds a little more buffer to AAoA in the future.
(3) The relationship element you mentioned. I suspect it helps in reconsideration if the rep can see you've held on to cards from that issuer, not only churned them quickly. It also might make it easier to get a loan from a bank, either from the approval process or the actual application process itself.
(4) Promotions - sometimes those disused cards will offer spending promotions.
(5) Those empty credit lines help utilization. But if you're carefully managing your pre-statement balances, that shouldn't really matter.
(6) Turning around available credit more quickly - for example, some people have to wait 6-ish months for Citi to release credit that was previously held on a card. But if the card can be closed during reconsideration, then the credit is available immediately.

These all have to be balanced with the occasional reports of people denied because their raw number of cards open was too high and also the possibility those cards may need to be closed in a mortgage application review.