There is a lot of interesting rumors here. From what I can put together:

-Costco does make some money on the debt portfolio of the card along with Citi (arranged with support by VIsa to make the final deal as discussed). Citi could lose money if none of the Costco cardholders pay interest, but the Costco cardholder is not that much better than any other card portfolio profile and enough of them charge too much on the card to payoff each month. Further, Costco puts friction in actually redeeming the Costco Visa rebates by forcing the consumer to visit the warehouse. Sure, there are some who convert to cash and walk out of the warehouse, but many just cycle it back in a purchase at Costco. I wonder if Costco puts more higher margin merchandise pallets in the store during the rebate redemption season.
-Costco has said its margin on gas sales has grown over the years (the first freestanding gas stations without a warehouse are opening). So increasing the Costco gas rebates is not a big deal. Let's not believe that Costco is primarily making money on the membership fee only. Costco makes real money on many items it sells and its ancillary partnership services.
-Aside from interest, the other important area of card revenue that is somehow shared by Costco and Citi is money made when the card is used at non-Costco places. This non-Costco retailer card use aspect is talked about in earnings calls more often than I expected.
-Costco does not pay zero Visa credit interchange. It is very low compared to typical rates, but not zero. It is accurate that every Visa issuer is dealing with this lower payment/share of the Visa interchange fee versus other charges (it isn't too different in concept than how an issuer would get a different amount for online purchases vs auto rentals vs in-store grocery stores vs. airline tickets, etc.). I haven't seen many Visa issuers penalize warehouse club use in their rewards earning programs (there are a few though), and they take it on the curve of balancing higher margin charges a customer makes versus use at warehouse clubs. I guess it is possible that a person could use a Visa credit card with a great rewards program only at Costco (and avoid paying interest), but I don't know of anyone who does that type of use only. I am sure there are a few Visa credit card customers out there at various issuers who are much less profitable than others because they don't pay interest, use their cards at very low interchange revenue places (really big grocery stores, government, etc.). But if this is a problem, we see what happens, the issuer just changes up the rewards program which has been happening quite a bit in the past few years to not reward these "unprofitable spending". I argue we often went many years without changes, but now card issuers feel very open to changing cards all the time -- and it is almost always to make the card more profitable or more difficult to maximize benefits.

Of course, it is weird that Visa got Citi for this deal because Citi is a really big Mastercard client (including launching what seems to be the first new super-premium Legend Mastercard), but there is a lot happening behind the scenes that we don't see including Citi Business or Investment or other treasury services that Costco has as a Citi customer.

I agree with others that this relationship as well as AA are very important to Citi, but at the same time, I don't see a lot of other issuers chasing large co-branded deals. We all know how much trouble Walmart has given its partners (Capital One/Synchrony), and some like Chase are doing just fine with whatever they have (Amazon) and their organic cards (where they don't have to share anything).

I think one of the things this card has which helps survival is that it really is not widely available, you have to be a Costco member. We see this with many cards out there like Robinhood, PNC, credit unions, etc. where it is rather difficult to qualify and obtain some of the higher reward cards.