This problem is easily solved. Treat all race rules presented in the PHB are for different cultures of mankind (humans). Just file the serial numbers off demihumans.SilvercatMoonpaw2 said:it's arrogant to assume that another creature cannot have the range of possibilities that a human can
Barbarians and wild men = dwarf stats
High society and university men = eladrin stats
Woodsmen and rural folk = elf stats
Common man and city dwellers = half-elf stats
[Secondary option available to all types of people] = human stats
Diabolists, cultists, and the cursed = tiefling stats
Monks and mystics = dragonborn stats (I don't really like breath weapons for PCs but this could be a Ki attack for monks)
...and you either keep Halflings as Hobbits or drop them from the game entirely.
An alternate option is to allow races to borrow each other's mechanics. Why couldn't a tough, stocky human have more in common with dwarf stats than generic human stats? Why couldn't a heroic dwarf have the same mechanics of a human and be a little different from his mainstream brother dwarves?