You don't need a more general opportunity attack mechanic to just say "if you run off at full speed they get a hit in on you." This is how fleeing from combat worked in all D&D previous to the introduction of formalized battlemats in 3rd edition. All it gets you is one hit, though, so it's not really sovereign against fleeing. But consider adding a rule to this effect (I think it's clear that in 5e they are trying to return to you the GM being in charge of the rules instead of the rules being in charge of you, so don't hesitate to add things in you deem useful).
To get out of a combat, characters can make a careful withdrawal or they can simply flee.
Withdrawing: When making a withdrawal, a character carefully backs away from his opponent (who can choose to follow). The character moves up to 1/3 his movement rate. If two characters are fighting a single opponent and one of them decides to withdraw, the remaining character can block the advance of the opponent. This is a useful method for getting a seriously injured man out of a combat.
Fleeing: To flee from combat, a character simply turns and runs up to his full movement rate. However, the fleeing character drops his defenses and turns his back to his opponent. The enemy is allowed a free attack (or multiple attacks if the creature has several attacks per round) at the rear of the fleeing character. This attack is made the instant the character flees: It doesn't count against the number of attacks that opponent is allowed during the round, and initiative is irrelevant.
The fleeing character can be pursued, unless a companion blocks the advance of the enemy.
Or better yet, AD&D 1e, which only has 2 pages of combat rules in total, and somehow we still all used and enjoyed it...
Participants in a melee can opt to attack, parry, fall back, or flee. Attack
can be by weapon, bare hands, or grappling. Parrying disallows any return
attack that round, but the strength "to hit" bonus is then subtracted from
the opponent's "to hit" dice roll(s), so the character is less likely to be hit.
Falling back is a retrograde move facing the opponent(s) and can be used in conjunction with a parry, and opponent creatures are able to follow if
not otherwise engaged. Fleeing means as rapid a withdrawal from combat
as possible; while it exposes the character to rear attack at the time,
subsequent attacks can only be made if the opponent is able to follow the
fleeing character at equal or greater speed.
a) You can add it and b) It doesn't have to be complicated.
Bonus: A slightly different take from Basic D&D's Rules Cyclopedia:
A character can only perform this maneuver
when he begins his combat round in hand-to-hand
combat with an enemy. The character runs
away from his enemy at greater than half his encounter
speed, up to his full encounter speed.
He forfeits the armor class bonus of his shield.
Any enemy attacking him later in the combat
round (that is, either an enemy who followed
him during the enemies' movement phase or an
enemy attacking with a ranged weapon) receives
a +2 attack roll bonus this round. This is the
same + 2 that characters normally get for attacking
from behind (see the Attack Roll Modifiers
Table on page 108).
If the character is not in hand-to-hand combat
with his enemy when his movement phase comes
up in the next round, he can go to running
speed that next round.
I kinda like that take on it because it takes a round to get up to top speed so there's one round of concentrated "Get him!"