While Dwarves getting Battleaxes, Elves getting Bows or Githyanki getting Greatswords and Medium Armor are also assuming the PC is a stereotypical member of these races, they are far less of a stretch than all humans learning to fight with Pikes.
Going down this same path with Humans is just a poor choice to balance the loss of their ability scores. You could have optional packages like "Dwarven military training" or "Guardsman training" that would give you that Proficiency package, but there should be a more generic alternative to it.
In general, Racial Abilities should be strictly genetic. Keen Senses for Elves, Fire Resistance for Thieflings etc. Skills and Proficiencies should only come from Background and Class. Hope One D&D corrects this.
Agreed. Spears and Shortswords would be a good pair for your standard human. Pikes and Glaives aren't exactly common, nor inexpensive, items.
