Here are some possible drawbacks which you might choose to use for balance:
Cost: You've said "all costs being equal", but this is a classic - a higher-level spell slot, perhaps.
Time: There's a tendency for area-of-effect (AoE) magic to be constant for anyone in the area, rather than instant upon touching the area. So a "zone of healing" works over time to heal your wounds, but can work on multiple allies at once. Or on enemies, if they capture the area.
Strength/Size/Duration: You can change it for different spells. In general, if A does everything B does and more, B will never be used where A is equally available.
Fixed effect/Status effect: If "Chill" in your example sets the temperature of everything in the area to 36° (1° below blood-temp), then it will substantially affect anyone there. If you set it to that temperature again, then ... no extra effect. The same would apply to a "Stasis" spell. Once it's applied, you can go on to less subtle "2d4 Cold Damage" spells.
Attention: Suppose the party has one healer who knows "Zone of Healing", but has to concentrate on it for as long as it will last. This might be stacked in theory, but if you only have one caster for it, you can't stack it in practice.
Crossing the streams: Another area-effect on the same area at the same time may injure the second caster unless the first one prepared for it. You can restrict this to only affect copies of the same spell, or only some spells. Or you could have your healer cast "Zone of Healing" on the foe's ground immediately, and let the opposing caster stun themselves or worse.
Lockdown: Non-stackable spells be nonstackable because they double as an anti-magic spell. This is good for locking down areas against opposing casters, at the cost of hindering your own mages. Helpful if you're up against an order of weedy mages but are working with big-club warriors.
Stickiness: Sometimes, you want to affect an area. Melt the ground, say. But sometimes, you want to affect the people in the area now, even if they move around later. Stackable spells tend to affect the area directly and those in it indirectly.
There are other methods you could use, but it's hard to say without more information about your world and style of magic. How common are casters? Can you cast the spell and move on to more magic before it expires? Are they fighting armies here or individuals? Are your spells very limited, or can you cast all day and into the night?