It seems to me, in my admittedly extremely limited experience, that a weapon with Reach is extremely powerful. They keep many enemies at a distance they can't hurt you, and if an enemy without Reach wants to hit you, they provoke an Opportunity Attack.
Is that right?
Realistically, that's probably all right. Weapons with greater reach, all other things being equal, do tend to dominate melee combat. In general, in a system, if an optimized pole arm user beats melee combatants of all other styles head to head, I'm generally not upset with that. Your millage may very here depending on what you like in a system, but that would be an example of acceptable imbalance to me.
So, what's the trade off? Why weren't all armies wielding pole arms? Well, aside from the fact that the spear wielder was the core of most armies, and the sword often the equivalent of a side arm or backup weapon, there are some advantages to a sword:
a) It's very difficult to properly employ a shield if you are using a pole arm. Generally, such techniques are confined to spears and perhaps pikes, which D&D generally models as not having the advantages in damage and flexibility of other pole arms. Without a shield, you are greatly disadvantaged against and vulnerable to missile fire.
b) It's a lot more unwieldy. A pole arm is generally about 7-9' long. This is a lot of weapon to be lugging around all the time and you can't ever really put it away or put it down. A sword can simply be sheathed and hang from your side until needed, freeing your hands to do other stuff. A pole arm is much more encumbering.
c) Similarly, it's significantly disadvantaged in tight quarters. Much of the advantage of a polearm assumes you either have another rank of pole arm wielders behind you, or else you have room to back up. If you don't have room to back up in, you can't easily maximize your advantage. If your pole arm is meant to be swung and you don't have room to swing, that can be a problem. If your enemy is pressed up to you chest to chest, the time to start thinking about dropping the pole arm and going for another weapon was a couple seconds ago. In ancient combat, this was typically a problem in mass combats where lines became crushed together. In D&D you add to that problem the fact you are fighting in caves or small rooms and similarly cramped areas.
I wouldn't be too surprised if 5e D&D models this to one extent or another. Typically, D&D has loosely modeled this. Polearms have always been quite powerful if properly used.
