The current system has a few major problems that look to clash with the game's design philosophy.
The first is flexibility. Why can't I trade my attack for extra movement? Why can't I attack first and then move? Why can't I trade my movement for something else? In real time, drinking a potion has no recovery. In turn based, it takes my single action for the turn.
Why is flexibility important? Because strategy is based upon decisions, and more flexibility equals more decisions.
The second is flavor. In real time I can fire a gun and then pause reloading to cast a spell. If I use a bow or a wand, I have to wait for recovery. This made me prefer reloading weapons for my casters, but that means forgoing a shield. Or let's talk about fast weapons. Sure, using a stiletto means I can act sooner.... but that won't help me take out targets faster. On the contrary, while I attack "faster", I will do less damage with my one single attack for the turn. This leads me to a third point:
Initiative does a nice job of showing how some characters act faster than others, but that is only half of what action speed does in real time. What about doing more stuff because you do it faster?
A fourth point would be that action balance feels off. A wizard can cast half a spellbook worth of buffs as free actions. Meanwhile drinking a potion takes your sole action for the turn (while it had no recovery in real time); granted, I understand being able to chug health potions or toss bombs as a free action would be a bit broken.
You could add a "Swift action" per turn to solve the latter, but a better system exists: Action points! We can even apply the whole recovery mechanic to boot! Six action points per turn, each corresponding to roughly one second real time. Recovery can "eat" into the ap you get next turn.
Basically you take real time and make each actor involved in combat act separately instead of all at once.