What can explain the D in Fridge but not in Refrigerator?

It makes it scannable by native English speakers, who would be tripped up by “frig,” and go a completely different direction.

The reason it’s missing in the long form, is that it comes from the Latin “frigus” for cold, and as you can see, it isn’t in there. We all just had to learn to pronounce the “J” sound instead of the hard “G”.