Well yes the mechanics of an issuer turning on the ability to 'BNPL' something after purchase is relatively easy, and has been done by issuers for many years (I think Amex, Citi, Chase all have had offerings live for years) but they have not made a dent into the integrated at checkout BNPL players. The interesting question is not whether they can create their own offering post checkout, it's WHY these offerings have basically been a 0 while the core BNPL players continue growing at 20%+ annually.
A few reasons:
(1) The offer AT POINT OF SALE is the product!! You need to offer this while someone is checking out for conversion to be impacted. It's a much harder change in behavior to say to someone "buy it like normal and then split it in our app". An installment plan activated in a banking app after you already bought the thing does none the conversion work. ... whether you think it should is beside the point. It's just clearly not a viable offer based on the fact that these products haven't worked.
(2) The economics are all wrong. What makes the BNPL at checkout model work is that the merchant is willing to pay fees because BNPL increases conversion and basket sizes. They're willing to pay ~4% on a pay in four txn vs. 2-2.5% on a normal cc txn. If you are Chase and offering an installment plan post checkout, you are taking on the same amount of risk as a BNPL provider, but not getting paid anything by the merchant to do so. For the group of consumers that would want to use this product, it becomes uneconomic (can you really compete with Klarna or Affirm when they get 4% from the merchant and you don't??) ... further, the lifeblood of the subprime issuers is the revolving interest on balances. Why would you transition someone from that highly profitable product to a much less profitable offering (installment loans). And if the issuers decided to charge substantial interest on the installment loans, why would a consumer use the product when they could get the same loan from Klarna or Affirm at a much better price because the merchant is paying a large chunk (or all) of the fee?
(3) Because you are underwriting every transaction, Klarna and Affirm can reach consumers the credit card companies can't. For example, a thin-file consumer can get accepted for a $200 bnpl loan but would never be accepted for a $5k line of credit. Therefore, if a cc company can't bring in a customer on a normal LOC, they won't be able to offer them this post purchase installment product either. The beauty of the BNPL model is the reunderwriting of every transaction.
the moat is that the loans are (a) merchant-funded (b) at point-of-sale (c) each txn is reunderwritten (d) signing agreements with all the merchants who have specific / custom terms that work for them and their customer base (e) the model puts Affirm and Klarna in front of consumers who have traditionally been excluded from the credit card ecosystem so there's a legitimate case that these consumers are incremental to merchants and improve conversion.