They stopped just 4 backgrounds short of every attribute combination

I'm sure I'm not the first to point this out, but it bugs me that their are 16 backgrounds and only 20 possible combinations of 3 attributes. They came so close to a complete set and stopped!

The missing combinations are:

STR, CON, INT

STR, CON, CHA

STR, WIS, CHA

DEX, INT, CHA

Naturally I'm planning to homebrew to fill the gaps (although this would require inventing new origin feats or using some general feats as origin feats), but I just don't understand why you'd come up with backgrounds representing 16 of 20 possible combinations and just stop short.

Anyway, I'm thinking SERVANT for Dex, Int, Cha with proficiency in Persuasian and Stealth. I haven't decided about the others yet.