There once was a day when the Sky Club was a "club." If Delta changes its policy to deny access to Sky Club members who are not flying on Delta, then it is really undermining the business model of even having a membership. Why would anyone pay for a Sky Club membership, when it is cheaper to gain access through a credit card? For many years, I have enjoyed the membership, such as in situations when I flew AS under the alliance and DL would deny access to credit card holders flying their AS Code Share flight, but still allow with the DL Sky Club membership. In addition, I have enjoyed having the DL membership as a way to access the AF Salon when I was flying DL out of IAD where there is no Sky Club. Similarly, I have used a United Club membership to access their club, when I fly DL out of SNA, where there is no Sky Club for DL flights.
Again, if I cannot be guaranteed access to a DL Sky Club, regardless of carrier that I fly, then I can simply drop the annual membership fee and continue entering the clubs for free using my AMEX Cent card which I will retain in any case, and which thus already provides me complimentary access on the margin. In effect, Delta is dropping the exact access policies that encouraged me to retain a paid membership, when I already have access through a credit card.