We also here reference to a Class F shuttlecraft. That suggests to me that the alphabetical classification refers to a type of vessel.
A Class J starship could also be an Independence
-class starship. The former refers to its type and the latter to its configuration.
In that vein the Enterprise
could be a Class A starship as well as a Constitution
-class Heavy Cruiser. These things needn't be mutually exclusive.
We know what a Class F shuttlecraft looks like. We've no idea what a Class E or A or L looks like. Are they more advanced or less? Does their intended primary function dictate their classification?