Given that some Spells have a different degree of damage depending on what level you cast them at. A cooldown system would not work. Also you can cast the same spell over and over again until you have now more slots available. You can cast Magic missile as many times as you have spell slots. If you take away from how the rules handle spells is it really D&D anymore.
Part of the way spells are chosen to be cast and what level they are cast at is all part of the D&D experience. So I vote on keeping spell slots in. When I go to cast a spell. I just click what spell slot I want to use from those that are available for use. Casting magic missile at 9th level is what I choose (or have to use because it is the only slot left). It is all about player agency.