This is how I'd like to see options presented in future editions for it:
Species - Your physical / mental characteristics and traits. Things like flight, elf trance, goliath size, dragonborn breath, etc. This would also have a 'custom species' option for players whose characters don't fit the norm. This would let you work with your DM to make more a suiting character while still being balanced (for example a dragonblooded human who has a fire breath ability).
Culture - The culture you were raised in. This would include some proficiencies, languages, and starting cantrips. So a dwarf raised in dwarf culture would speak dwarvish, have axe proficiency, and be knowledgeable about either stonework, smithing, jeweling, or brewing. A dwarf raised among elves would speak elvish, be more perceptive, and know a cantrip.
Profession - What you did before you were an adventurer. This would give you some tool proficiencies, skills, maybe languages, starting equipment, and an ability.
The combination of these should allow players to really make a character which fits.
Additionally, in all these sections, there should also be an option to help a DM and player work together to make custom options in case the default ones don't suit, and allow players to really go against the tropes.
(I'd also like ability score modifiers on each, but it's clear that's not the direction in which things are going).