Actually, it is even 'worse/better' than real-time... I am actually messing with the idea of letting the player choose when to take a turn.
The way that will all work out is still a bit drafty at this stage, but the general idea is this:
a Gauge fills between 0 and 200%
You can interrupt that gauge at any time to take a turn (I'm thinking not before 25%...)
The action you take is modified by the % of time waited (100% = regular damage and effects, and you get + or - depending on how long you've waited).

There is no 'random' but damage always changes based on time waited.

I think this adds a bit of depth to this whole strategy build.

I think you have a good system going. I can see lots of tactical possibilities. It reminds me of Valkyrie Profile in a way. Though, you might want to change cooldown from turns to seconds, else players will spam skills at 25% to regenerate the big one faster.

Something else you could consider is wind up and cooldown periods. Wind up is a delay between player selection and skill activation. Cooldown is a delay between skill activation and the moment the player can take another turn. The total skill time is equal to wind up + cooldown. This allows you to design skills with a fast wind up, but much longer cooldown. For example, the player can choose to have the skill activate now, but have the next turn start in 8 seconds or hope nothing will happen in the next 4 seconds before the skill activates and have the next turn in 5 seconds.

Actually, I'm already using wind up.
But the technicality here is that cooldown is independant from players taking a turn.

Between choosing a command and executing it, the player has no control over the character.
But during cooldown, the player may take other actions until the cooldown for a specific skill has elapsed.
This is why I use both.
So technically, I'm using a wind up, a cooldown, and a skill-specific cooldown. That may look like much, but it is rather fluent in-game.

And thanks!