Combat in general will not be much different
Your house-rule makes the Disengage action much worse, but because this action is not used much, the effect on the overall combat will be limited. In other words: most combats are very stationary, so an incentive to move less simply won't have a big impact on the game.
When someone has to move past multiple creatures no matter what, they will just use the Dodge action instead of the Disengage action.
The only big exception are:
Creatures that can Disengage as a bonus action
These creatures include NPCs such as goblins and playable characters such as Rogues and (to a lesser extent Monks). These creatures are designed to easily avoid all opportunity attacks. Disengaging as a bonus action is a core defensive and offensive feature which your house rule weakens significantly. As such I think that your house-rule should not apply to bonus actions.
Your house-rule does not solve the problem you described
it makes no sense to me that backing away from enemies in front of you somehow makes you immune to all other opportunity attacks regardless of direction.
the Disengage action will only prevent opportunity attacks by enemies within melee range at the time the action is taken.
Your house-rule basically narrows the 'range' of the Disengage action, instead of the 'direction'. Notice how it does nothing to solve your problem as you've described it.
Usually , D&D 5e does not track which way creatures face, so stuff like "in front of you" has little to no meaning. However, there is an Optional Rule for Facing in the DMG (p252), into which you could integrate a Disengage house-rule that actually solves your problem.
Your house-rule is based on a wrong assumption
You assume that disengaging means "backing away from enemies in front of you", but that is simply not the case. The Disengage action makes no sense to you because of this incorrect assumption.
The Disengage action says:
If you take the Disengage action, your movement doesn't provoke opportunity attacks for the rest of the turn.
As you can see, nowhere does the disengage action mention a direction. When you disengage, you aren't merely "backing away from enemies in front of you", you are doing your very best to move without exploitable openings for the rest of the turn.
Overall, I do not think this house-rule is worth the trouble because it won't change the game much at all, besides nerfing Rogues. Moreover, I question whether you can get your players on board with a house-rule that does not solve the intended problem and that is based on an incorrect assumption.