I disagree with a cooldown like this. To be honest this will make the game potentially pay 2 win.
My reasoning for this is one simple thing:
Pyro kit.
It doesn't have food because it is focused on one thing: High as frick damage. At default level (no rank) it is quite bad where it's power doesn't do much, but at emerald level it makes the damage WAY higher, allowing for ridiculous damage as well as pyro getting better armor for protection and fire resist. In a battle where you cannot heal, and the enemy does 2X your damage then you are basically done for. And this damage is only avalable to emerald level the game is basically pay 2 win. Yeah so unless you want all PVP games to die, don't do this.
Also once Vertx made this optional for a food cooldown and people hated it and it got removed in like 2 days.