Kinetic Weapons Are Just Better/Analysis
A theme in many science fiction works, especially newer ones. It is not a bad thing: in older science fiction, portrayals of energy weapons were usually very inaccurate, showing them as simply better because they were more high-tech. This is a surprisingly common misconception: if a category of technology is more "advanced", it must be better than something less "advanced." This is the same logic that has Star Trek medical isolation use "high-tech" forcefields instead of boring old walls, despite the fact that boring old walls don't vanish if you unplug them.
Real life energy weapons haven't really made it far from the labs just yet... they need too much power, and they generate too much heat. They're expensive, fragile, often require masses of highly toxic, corrosive and explosive chemicals to function, and honestly just don't work very well. High power lasers are still just not high power enough. Particle beams work very poorly in an atmosphere and are too hard to focus over long distances, even in a vacuum. Anti-personnel microwaves aren't as effective as conventional riot weapons, and small lasers that blind people don't sit well with the Geneva Convention. Decades of research still hasn't produced any small arms better than automatic rifles... weapons using chemical propellants are just more effective (that's why they are used), and this situation isn't going to change any time soon.
Kinetic weapons also have one advantage over energy weapons: the ability to use indirect fire beyond visual range. Due to slower projectile speeds compared to energy weapons, kinetic weapons usually never reach escape velocity, and what goes up must come down. Thus one can rain death upon the enemy beyond the horizon or over large mountains/rocks/hills. Someone, however, is needed to relay information of the target's location back to the weapon.
And to top it off, in the long run, even when the energy weapons will finally reach maturity, kinetic projectiles will still retain one critical advantage: while energy weapons will always need a some form of emitter, however advanced, good old slugs can always accelerate themselves, pretty much indefinitely as long as fuel holds out. Relativistic kill vehicles are the most effective means of destruction possible: after all, any weapon is a means of transferring the energy from the source to the target until the latter breaks.
For the Wave Motion Gun you need to consider the heat balance, design complex energy conduits, build labyrinthine cooling systems (often with very conveniently placed exhaust vents), etc., each of which would waste some of the energy as per the laws of thermodynamics. For the RKV you can simply hook the reactors to the engines of your slug and say goodbye to your enemies. At the speed of ~0.87 c, the kinetic energy of the massive body exceeds the energy that can be achieved by annihilating it with antimatter of the same mass.
As a technical note, Kinetic Energy = gamma*mc^2 where gamma is the Lorentz-Boost Factor, or gamma = root(1/(1-(beta)^2)), where beta = v/c. Annihilation energy = 2(mc^2), because the matter and antimatter each carry a rest-mass-energy of E=mc^2 and energy is conserved. Mass energy goes in, explodey energy comes out, with the same total energy. Then cancel terms and you're solving for gamma = 2, which has beta = .866.
Another consequence of physics in this regard is that not only are the more exotic kinetic weapons longer to build up more speed (railguns, coilguns, and so forth), but the ships carrying them must be more massive so as to do themselves less damage in firing weapons off due to conservation of momentum. That is, a very light ship with a big projectile will accelerate itself backwards when it fires, which is known to be detrimental to things like pilots or internal structure. Therefore, massively large ships may be justified as what amounts to artillery pieces, even though more mass is detrimental to fuel efficiency and rate of acceleration. This may imply that kinetics-based ships are a valid example of of tiered scifi fleet.
This is not to say that energy weapons are completely useless, however. At sufficiently great distances, even the numerically small difference between .99c and c proper can make the difference between a hit and a miss. There are good reasons why research into anti-missile defence is headed into lasers. Ammunition will also run out, barring things like Star Trek replicators.
The point of >=0.87c impacts exceeding the power of antimatter also only applies if it is practical for the society in question to employ kinetics that can achieve such muzzle velocities. In a world where practical mass production of antimatter is possible but not high-level kinetics - Mass Effect, which has antimatter but even big dreadnought-mounted spinal guns' muzzle velocities max out at 1.3% of lightspeed, comes to mind - having payloads would remain useful.