Part of the difficulty of the future of space warfare using kinetic projectiles is that they don’t stop, or slow down. If a gunner misses the intended target, that shot will continue on ad infinitum. That projectile will travel on at its incredible speed, like an angel of death lost in the void, waiting to meet a victim. Imagine you are a simple freighter, carrying futuristic goods of simple, yet important nature to your fellow living beings across the universe. By all indications the route you are taking should be a safe one, until your ship is obliterated by a bullet shaped Buick travelling at light speed. The bullet had been intended for a warship during a battle that had occurred long ago and far away, but no matter, you were still in its path and therefore you must die.
Now, given the distances between star systems, a projectile launched at even light speed (a velocity I already mentioned is highly unlikely to be achieved even in the distant future) it would still take years to reach even the next star system, let alone the next inhabited system. And that is, of course, provided the bullet just so happened to be fired in the exact direction of a star system, and not straight off into the black nothingness of space. Therefore, mathematically speaking, the likelihood of said futuristic bullet even hitting a planet of any significance to the future space fairing denizens of the universe is unbelievably small. Smaller still the likelihood of hitting a moving ship.
Ah, but math is a fickle bitch, especially in matters of life and death, because on a long enough timeline, anything that can happen, will happen. True, the likelihood of Bullet Number 1 hitting the space freighter USS Some Ship is, indeed, infinitesimal. However, no war was ever won by a single bullet (especially one that missed the intended target), and no war ever proved to be the last. Probability is cumulative so long as the chance continues to be taken, and eventually the arithmetic begins to add up. As more and more wars are fought, and more planets colonized, and more trade routes established, and more freighters take to those shipping lanes, soon the dynamic begins to change. Soon the probability the any bullet will hit any ship or any inhabited planet becomes really rather high.
Of course, one random freighter getting obliterated by a stray shot from a hundred years ago won’t change much. After all, it’s just a freak accident. Until Math rears her ugly head again, and reminds us that time is infinite, and our model is cumulative. Likelihood continues to increase until it is no longer a freak accident and is now a rare occurrence. And then likelihood continues to increase until it is no longer a rare occurrence and is now an emergent problem. From emergent problem it becomes a known issue, and from known issue it becomes an epidemic. Soon it is a daily occurrence for someone somewhere to have to deal with the impact of a death Buick from a thousand years ago launched at some unknown enemy in some unknown battle during a war long forgotten between peoples that probably no longer exist.
From a societal perspective this would launch a campaign to change warfare. The people of the future would likely treat solid ballistics much like we treat landmines today. Claiming them to be irresponsible and dangerous, they would push for weapons like lasers that inherently dissipate over distance. But results would come slowly, because by the time the problem became big enough to require action, there would already be tens of thousands of years worth of death Buicks flying around the galaxy, just looking for some poor colony to crater.
And thus the wheel of peoples’ lack of forethought causing the future deaths of their innocents would continue to turn. Much as it always has, just with a different face each time.