To the does it matter what rodent is fed? Well it depends.
While it’s true that there is a difference if you compare identical size mice and rat with animals like BP who transition from one size to another fairly quickly I do not find it to be a concern short or long term. I start everything on mice because they are more enticing however after the 3rd meals everything eats rats and I used to start snakes on rats with no issue.
Now with some adult colubrids and other adult smaller snakes it would be different, for example if the maximum prey size is an adult mouse, it would be preferable to feed adult mice compare to rat pups especially since you are looking at long term. Mice have more protein, less fat and are better suited for smaller snakes that feed on smaller preys during their entire lifetime. Rat can be offered but I would suggest to keep this an occasional treat especially with species like hognose etc
As for the "spongy" claim if it was the case their would be a lot of "spongy" snakes out there (whatever that means)