It really doesn't. Barrier soft-countered ignite because it nullified all but one tick of true damage, heal counters it harder because, even with the reduced healing, it still provides a speed boost that allows a disengage, plus provides a health buffer to counteract the majority of ignite's damage. Plus it scales better in to late game by providing greater mobility on a squishy carry, and heals more overall than ignite deals damage.
I've found the best setup for bot is heal on adc, exhaust on sup, as heal has greater offensive capabilities than exhaust and doesn't require getting into dangerous ranges to activate it effectively, so it's better on the adc. And exhaust is really powerful right now, and supports will almost always be face to face with a dangerous target, making it easy to make the most out of the damage mitigation, provide additional soft cc, and lowers risks of taking kills from adc.
Ignite really only has a place against heavy heal teams, and that would be on, at most, top mid and sup. Against a team with no real heals though, I've always found no ignites with top tele/exhaust, mid heal/tele/exhaust, sup heal, and sup exhaust, provides a nice mix of defensive and offensive utility that scales really well to late game because ignite's dot becomes almost invisible when people start blowing up in 2 seconds, and no heals are around to truly justify it.