It'd be very different to say the least...Savage Worlds takes this approach, as does GURPS, I believe. Wasn't there a racial "rarity" list being discussed for 5E at one time?
What races are we looking at being in the PHB if they go with "has to have been in a PHB(1)?"
Human
---
Elf
Dragonborn
Dwarf
Gnome
Half-Elf
Half-Orc
Halfling
Tiefling
If we included later PHBs, we'd also have (not counting subraces that don't have their own unique name):
Deva (4E)
Drow (UA, 4E)
Githzerai (4E)
Goliath (4E)
Svirneblin (UA)
Duergar (UA)
Minotaur (4E)
Shardmind (4E)
Wilden (4E)
---------
Campaign Specific
Awnsheglien/Blooded (BR)
Bariaur (PS)
Caliban (RL)
Changling (Eb)
Dragon (CoW)
Genasi (FR)
Githyanki (PS)
Hengeyokia (OA)
Kalashtar (Eb)
Kender (DL)
Korobokuru (OA)
Mul (DS)
Nezumi (OA)
Shifter (Eb)
Spirit Folk (OA)
Thri-kreen (DS)
Warforged (Eb)
Vanara (OA)
BR = Birthright
CoW = Council of Wyrms
DL = Dragonlance
DS = Dark Sun
Eb = Eberron
FR = Forgotten Realms
OA = Oriental Adventures
PS = Planescape
RL = Ravenloft
UA = 1E Unearthed Arcana
...and these are just the ones I remember and not counting fiddly subraces (such as Gold Elves), campaign world variants (like Dark Sun's cannibalistic halflings) nor supplemental books like Expanded Psionics, Races of... or books like Incarnum.
I think it's pretty obvious that just covering the PHB races from all editions is going to have them pretty occupied.