I know cleave isn't an existing thing in 5e - it's Larian homebrew. I don't have an issue with what they're letting character's do, it's how they do it.
The special weapon attacks totally feel like something a battlemaster fighter or maybe a kensei monk could already do. So make it a class feature of fighters (or a subclass, or all martial classes) that they can do fancy moves based on the weapon they're wielding. It could either be limited (once per encounter or long rest or something) or be unlimited with a tradeoff (this attack does less/no damage, but also knocks the target back 5 feet). There are ways to implement homebrew rules that make a character feel special because their skills allow them to do a cool thing that most people can't. But if everyone can do anything so long as they pick up the right item, what's the point of characters having classes and strengths and weaknesses?
So basically add these weapon abilities to the list of Battlemaster maneuvers? That list already has trip, and most maneuvers are already Smashing because they deal the extra superiority die damage, so we'd be adding Cleave and Charge.
At some point we have to draw a line between class skills and general/equipment skills, because if you go far enough ~everything could be a class skill. E.g., Shove. One could argue that only martial characters should be able to shove, as only martial characters have trained in melee combat to make such an attempt without it utterly failing or opening themselves up to counterattack. I think that these limited-use weapon abilities lie closer to Shove than to class-defining abilities like casting spells, sneak attack, or bonus action dashing.
But I see your point. It is a somewhat magical/supernatural ability given by the weapon, instead of an ability given by training/class. I just think it's not offensive enough to warrant removing.
