Just as a nice round example number, let's say someone is effectively paying a 1% fee at time of purchase.

How do you turn that into an interest rate? Stuff at the start of the month and stuff at the end of the month are going to pay interest for different lengths of time. What if they change the timing of purchases?

Let's say you pick an average you're satisfied with. Okay, now you've calculated a rate you need to charge for the first month to match the old fee. You have to charge this specific percentage for the first month to make the math work out. ...but what if that percentage doesn't match the percentage you used to charge after the grace period?

One way to resolve this is to charge a first-month interest rate and a subsequent-months interest rate. But that's not really an "interest rate" anymore, is it? You're just obfuscating the fee, and the goal of this exercise was to make things more transparent.

The other way to resolve this is to have the "interest rate" change every single month, based on the timings of when you did all your purchases. This is just taking the old system and hiding it inside a black box, and that black box spits out an "interest rate" each month.

Unless I'm grossly missing something, there's no way to use just an interest rate to emulate a system of upfront fee plus interest rate. Do you have a suggestion of how to make the math work? Tell me what interest rate could replace "2% fee, 1 billing cycle grace period, 16% interest afterwards". Also tell me what interest rate could replace "0.5% fee, 1 billing cycle grace period, 16% interest afterwards".