Normally, I would be entirely against cooldowns. But in D&D 5e, there are MANY abilities that are balanced by the fact that they are recovered not by long rests (sleeping for 8+ hours), but by short rests (1 hour).
I would not be against having short rest abilities (including the Warlock spell slots) recover after every combat (either automatically or with say a 1-5 minute real-time cooldown.
The Warlock in particular is balance around the whole short rest mechanic; Warlocks have almost NO spell slots, but make it up for being able to recover ALL their spell slots with a short rest. If they throw out the short rest as a mechanic, and force Warlock to only regain their spell slots with a long rest, it will severely harm the class.
And Warlock is not alone. There are many classes that have features that rely upon the short rest mechanic.
So if they get rid of the short rest mechanic and don't implement a cool down system of some sort, it will result in the 5 minute adventuring day; which in my opinion is worse than a cool down mechanic.
Do anything BUT cooldown; Put reagents, limits to 3 short rests in between a long rest or something similar but cooldowns are the WORST, most immersion breaking mechanic and should't exist.
PS : WLKs only regain spells up to circle 5 in a short rest.