Actually it might have some benefits, but it could not replace missiles or kinetic energy weapons. The other comments have contributed a lot to the answer, so I'll limit myself to things that have not been elaborated as much.
The most important factors at play in the (drag-less, atmosphere-free) space environment, become 1) Destructive power, which could be modeled as energy per second per surface area of the target (plus, in the case of massive projectiles, momentum, which becomes extremely important) and 2) Accuracy.
As far as -1- is concerned, some important aspects have already been mentioned. Kinetic energy weapons (such as PDCs or rail guns) will impart a large amount of energy with every hit. In space, there is no drag to slow down projectiles and thus no energy loss as the projectile travels. The potential of the laser to achieve a similar result depends on the available laser power. Theoretically one could build a more powerful laser, or a particle-accelerator weapon (shooting high energy protons for example -effectively a plasma weapon), the question is whether that is feasible with the technological resources available in the Expanse universe. The kinetic weapon delivers its energy on impact, giving extremely high power per surface, making it effectively destructive. The impact will create debris, that in turn will continue the destructive propagation of energy further, as momentum is conserved. A laser beam imparts very little -insignificant- momentum to the target. Even a plasma weapon would impart insignificant momentum. The after-effects of momentum are a crucial aspect of the weapon system.
Divergence, diffraction, are subjects I can't really talk about. Different lasers (or energy weapons) would potentially have different characteristics, in principle it's possible to achieve minimal divergence over ranges where the weapon can be accurately fired.
For the weapon to be effective, the energy must be transferred to the target, and even better to a specific location on the target when possible. Spreading the energy on a large surface is undesirable, since it will minimize the destructive effect. The rail gun seems ideal in that respect. Bullets usually hit in different places, similarly it is very difficult -probably impossible- to keep the laser beam on the same spot for long, given that ships rotate and accelerate in different ways. Very short powerful bursts would be more effective.
If the target's range is below 10 km, it is most likely possible -always depending on relative acceleration- to aim the laser on the target for short bursts (to maximize power/surface). As the range increases, it becomes harder. At a range of 100 km budging even for 1/100 of a degree would bring the laser 17 meters off target. So it depends on the ability of the engines and the weapon system to achieve and maintain an exact orientation and target alignment in combat conditions, the error margins of the navigational instruments etc. Shutting off the engines before targeting and firing would put the ship in free-fall, achieving its maximum accuracy.
I am not aware of the capabilities of current thrusters to achieve and maintain orientation, so I'd avoid making an educated guess. Maybe it can be done with arc-second accuracy, but under what conditions (and given how much time to perform the alignment). Using an autonomously targeted laser (ie one with a target acquisition arc, on a mount that can accurately track the target in this arc), would eliminate the need for accurate thrusters -but only during free-fall.
As ranges increase, active or semi-active guidance homing missiles would be preferred.