Allows you to take on a uniquely designed persona of a fictional character
How unique does a rpg character have to be? Totally original or simply noticeably unique from other characters being played in the campaign?
If there is only ever one Half-Elf Paladin in the campaign that character is certainly uniquely defined by being a half-elf paladin.
I've played the Dallas RPG the characters were predefined and it was actually fun as long as one could get into soap operas. Same with various superhero RPGs, most of them are more fun with "name" heroes.
A Lewis and Clark rpg could be fine and dandy. One needn't play the persona of a fictional character at all.
Provides rules for improving that character
The existence of a persistent universe makes improving a character possible. Acquiring wealth, influence and fame are all methods of character improvement .
In OD&D character improved by gaining levels, acquiring wealth, finding magic items, acquiring followers and henchmen and building a stronghold.
In classic traveller a character improved by gaining wealth and building social contacts.
Provides rules for task resolution, including combat
This is completely and totally covered by telling the players it's the GMs role to determine the odds of success for things not explicitly covered in the rules. Such a statement is surprisingly enough an explicit rule that covers task resolution.
Provides rules to help the GM adjudicate social interaction
Social interaction is covered or assisted by the rules in any game that provides a social score - D&D has always done it with Charisma. One needn't even use the "reaction table" which could cover a vast range of social interactions, one would just need to keep mind in the Charisma score.