I can't find anything in the PHB that actually says that Monks are proficient with unarmed strikes by default. Their Proficiencies list just says simple weapons and shortswords. Their Martial Arts ability says it gives them "mastery of combat styles that use unarmed strike..." but not actually proficiency.
Am I missing something, or is it actually correct that Monks don't have their proficiency bonus with unarmed strike unless they get the proficiency from a feat or something?
In the errata for the Player's Handbook, the Unarmed Strike entry was removed from the weapon table. However, the rules on Unarmed Strikes in the combat section now say that every character is proficient with unarmed strikes (emphasis added):
Instead of using a weapon to make a melee weapon attack, you can use an unarmed strike: a punch, kick, head-butt, or similar forceful blow (none of which count as weapons). On a hit, an unarmed strike deals bludgeoning damage equal to 1 + your Strength modifier. You are proficient with your unarmed strikes.
Unarmed strikes do not count as "Simple Weapons" - they don't count as weapons at all. They were originally listed as Simple Weapons in the first printing of the PHB, but this was a mistake that was corrected in the errata.
All characters of all classes are proficient with unarmed strikes. The last line of the Melee Attacks section on page 195 of the 5th edition Player's Handbook, second printing (as of the 2015 errata), states:
You are proficient with your unarmed strikes.
For clarification, in the 5th edition it does not say this under simple weapons (where "unarmed strikes" are no longer listed, as of the same errata); nevertheless, all characters are proficient with unarmed attacks.
In addition to being listed as a weapon in the starter guide, in the PHB the monk description explicitly mentions it. The monk level table spells out the increasing base damage that a monk does unarmed.
