In D&D 5E different races have different movement speeds.
From the players Handbook:
Dwarves, Gnomes and Halflings can only move 25 ft in a round.
Wood Elves can move 35 ft. in a round.
Everything else has a speed of 30 ft.
Monks get bonus movement as they level up, moving an extra 10 ft. per round at level 2 and an extra 20 ft. per round at level 10.
Barbarians get Fast Movement at level 5 which is an extra 10 ft. extra movement per round.
The Mobile Feat can also increase your move speed by 10 ft. per round.
There are spells that can increase your movement speed and actions like dash that allow you to go farther as well.
Giving everyone run would make these pointless abilities so it is unlikely that they would give run to everyone the way they did in Divinity 2.