If all spells require the same "fuel" you will most likely end up with using the same spell all the time, the best spell in its respective category.
There would be no incentive to use other spells. Cooldowns are an easy way to avoid that and help to differentiate spells further.
The answer to that problem would be to have the spells different enough to be useful in different situation. If I have 3 damage spells, one dealing 50 dmg, the other 30 and the last one 15 then I don't see how forcing me to circle through them makes the game more interesting.
Just like i reduced mana systems to its worst outcome, you are reducing cooldown mechanics to their worst outcome, i.e. causing simple cycling.
I agree that in this case nothing is won, but cooldowns can interplay with the dynamics of the battle. If it is well designed it might not be
the best option to cycle through them nonstop but to consider when you should use them and what you are risking if you put your best spell
on cooldown right now. Cooldowns and Mana aren't even opposites and can be used together.
But if you wait for the perfect moment to use a given spell you risk a situation where you could use that spell and have it restored by the time you needed it. For example you put-away using charge which has 2-turn cooldown for 5 turns waiting for a good opportunity only to realize that you've wasted on charge by being indecisive. Which is why people end-up cycling through their best abilities.
If your goal is to make players hesitate before shooting away all their best spells then the old vancian system or limiting their per-encounter use is better.
I don't play PnP but the games that come to mind (BG, IWD, NWN, PoE) did a poor job at making you hesitant at using your spells. You can most of the time
blow away your best spells in each encounter since resting is often possible in between. Instead of cycling you get a single iteration from top to bottom.
I have replayed BG2 with SCS and Ascension not to long ago and at higher levels you have so many spells and HLA's that fights are over before you can even
empty your lvl 8 and lvl9 spell slots.
I don't think that a Vancian/slot system is inherently better than a cooldown system. Both can be used as tools to design good combat mechanics,
they don't exclude each other and could be used together.