A few thoughts on the question at hand coming from the point of view of an unarmed martial artist who has only relatively recently (in the last couple of years) transitioned to European sword arts:
While the side kick is (often) more powerful it leaves the attacker far more open to counter attacks - particularly off balancing in either direction along the lateral line, or movements out to the attacker's rear (as the hips are side-on during the course of the attack). This is particularly true if the counter is a ringen manoeuvre - many of the wrestling techniques seen across the sources would be ideal, in fact.
Similarly continuing the offence, or retreating in defence, is difficult with a side kick as the feet are off their normal line of movement, as are the hips, making transitions in motion difficult (and in some cases entirely impractical).
Put together this means that a side-kick is a technique which can only be employed under certain circumstances with full effectiveness - a notion borne out by the relative infrequency of side-kicks in full contact unarmed bouts when compared to the front kick.
Conversely, the front kick is by far the most versatile kick and is frequently seen in most all martial art. It can be used to distract in readiness for a follow up, to create space by pushing the opponent back, or to actively damage the opponent. If it is interrupted it can quickly be turned into a passing step, and it is a natural movement which doesn't rely on the flexibility that a side kick does.
Also, because the hips are not off-line the sword in the hands is still in a position of readiness and can be used to simultaneously attack or defend while kicking, and even acts as a passive defence and major distraction during the course of the kick.
Front kicks can be delivered in an arc motion (generally notable as groin kicks) - though occasionally higher arcing kicks are seen, particularly in Chinese martial arts. However, these are much easier to avoid than a thrusting kick action (the fixed arc is easy to predict and move out of range), and have a more limited range of targets (groin, inner thigh, chin, etc). Swinging kicks are also less versatile as they impart momentul which is difficult to control and mutate into other techniques, and which interferes with the action of the hands, particulary when using a sword.
All things considered, using a sword in combat is taxing enough without having to slot in kicks for esoteric situations - for a simple go-to technique which can be relied upon, front-kick is king.
Edit: had to add this: