I've had to do chargebacks with two different banks and both were painless even though something was delivered.
But at least the other time a merchant pushed back on a charge back, it worked out better. A South American airline charged me for a flight between two cities in a continent I had never even been to in my life. They used as proof a record that simply showed the flight did actually fly. My bank sided with me.
Long story short, don't threaten lawsuits. Just file the suit.
And as someone who litigates for shits and giggles, it can be pretty expensive in Small Claims, about $400 often just to file and do service on the defendant. And some courts won't accept suits that are less than the filing fee. And a lot of the time you can't get back your costs from the defendant either. And.. I'm not sure you can sue the bank for not charging back. I guess the correct process is to sue the merchant for never delivering the merch.
I bought some electronics, turned out it was a scammy company. After six weeks, nothing shipped, merchant agreed to refund me. Asked card company (Cash/Square/Block) for a chargeback. Week later merchant ships something, FedEx fails to deliver and it gets returned to merchant.
3 months later Square asks me for all documentation. I give it to them. They say I can't have a refund as the package was delivered. I tell them "yes, delivered back to the merchant". They say "sorry, our policy is that if it was delivered somewhere then we won't do a chargeback. I know that's not the outcome you wanted." Then they terminated my account. LOL