Back when it did, champions with suppressions were hard countered by taking a summoner spell.
QSS however, is more expensive overall to get, both in gold, time, and slot efficiency.
This gives players with suppressions period in which they have some of the most powerful ultimates 1v1, while still giving a method to fight against them. Additionally, it doesn't make their ultimates useless as they use them on people without QSS or wait until they've been used on weaker forms of CC and disables.
QSS gives timing windows for playing with and against suppressions. Cleanse gives shallower windows and tends to make suppression champions unplayable if it removed their ultimates.