There was a recent "Got any horrible DK game ideas?" post and I wanted to contribute this but it was too long
It's established that Cranky Kong was the original Donkey Kong in the initial arcade title in 1981.
This implies "Donkey Kong" is a title, meaning the current Donkey Kong inherited the title from Cranky (and Donkey Kong Jr.); he is simply the current Donkey Kong. A power struggle for this title would open up an entire world of Kong lore.
In this game, Funky Kong competes with the established Donkey Kong for the role of "Donkey". He is clearly the superior Kong and he deserves to be the Donkey Kong more than the incumbent ape. The ensuing struggle would result in a massive rift in the Kong family, spurring on unlikely alliances, reluctant betrayals, and ultimately letting the players see the Kongs make complicated, morally compromising decisions on an emotionally intricate level we've had yet to experience from them.
Funky's superiority has been acknowledged or at least referenced in nearly every title he is present in. For example, in his very first appearance in Donkey Kong Country in 1994, his theme music includes an intriguing Easter egg:
(see https://www.youtube.com/watch?v=A8mgAP-tTF0&t=39)
The sound that plays at the end of drum fill before all the other instruments come back in is none other than the "oof" sound DK makes when players lose a life. This is a subtle nod to the fact that the developers were confident Funky Kong could easily decimate the standing Donkey Kong. In Tropical Freeze, Funky Kong has five hearts, whereas Donkey only has two, making it abundantly clear that Funky is more than twice as resilient.
Donkey Kong 64 also makes it clear that Funky is in charge of the Kongs' Armory. His unique position as warden of weapons and ammunition puts him at an even greater strategic advantage should he ever decide to declare war.
In addition to his imposing presence and unlimited access to firearms, Funky Kong seems to have a vast intellect, suggesting he could very well be a proficient tactician. He was a mechanic in DKC3, demonstrating he is knowledgable with a variety of vehicles and custom modifications. Moreover, a series of videos posted on YouTube have documented many of Funky Kong's social interactions, which demonstrate considerable levels of cognizance for an ape, including (but not limited to):
-helping someone recover from a panic attack in a public restroom
-offering consolation after a messy divorce
Given this level of manual dexterity, social awareness, and foresight, Funky Kong is undoubtedly a worthy adversary--especially for Donkey Kong, who rarely even speaks in full sentences.
Undoubtedly, the only reason Funky Kong has yet to challenge Donkey Kong is his generally "chill" demeanor. His relaxed, laid-back lifestyle forfeits the aggression necessary to pursue what is rightfully his. However, it wouldn't take much for him to realize his skills and abilities far exceed DK's, and the ensuing battle would pit all of the Kongs against each other. Below is an outline of where some significant individual characters might end up in the conflict and why:
Team Donkey Kong:
-Diddy: DK's most loyal friend and confidant. Diddy wouldn't dream of letting the Kong Kingdom fall into disarray. He refuses to acknowledge Funky as the superior Kong and will stand his ground, despite knowing in the back of his head that they are destined to lose.
-Dixie: despite harboring a little resentment over having to rescue DK on two separate occasions (once accompanied by an actual infant), Dixie sides with DK because 1) Diddy did, and 2) Tiny sided with Funky, and Dixie is excited by the prospect of punishing her for replacing her in DK64
-Chunky: even though he is one of the strongest Kongs (perhaps stronger than even Funky himself), Chunky is a pushover and was simply goaded into swearing allegiance to team DK, which he did reluctantly.
-Squawks: Donkey Kong's most loyal advisor would refuse to leave his side in battle; he's the Zazu to DK's Mufasa.
-Swanky: he seeks to maintain the status quo as anything else would threaten his status and wealth
-Wrinkly (ghost): as a benevolent spirit, Wrinkly would not be of any value in a direct combat scenario. However, her advice from the beyond might give team DK the upper hand in some specific instances.
-Candy: Donkey Kong but with big ol' boobies
Team Funky Kong:
-Tiny: a devoted Anarcho-primitivist, Tiny Kong will do everything in her power to challenge authority. Once Funky resolved to claim what should have belonged to him all along, she realized an opportunity had presented itself to challenge the one untouchable authority and she is taking it.
-Lanky: due to the Manky Kong betrayal of the Primate Alliance during the Great Ape War, most orangutans have been outcast from the Kong family. Lanky feels resentment over DK's handing of these events, and the fact that the rest of his kind are still rejected by the other Kongs would compel him to avoid team DK (source: https://donkeykong.fandom.com/wiki/The_Great_Ape_War)
-Kiddy: idk he's a baby
-Rhambi/Enguarde/Expresso: decades of resentment over being ridden on and exploited have incentivized these animal buddies to side with Funky: he respects them and sympathizes with their plight. Furthermore, Funky has no reason to ride on animals because he has a floating surfboard and can craft his own vehicles.
-King K. Rool: "the enemy of my enemy is my friend"; both share the common goal of dethroning Donkey Kong. A tentative allegiance between K. Rool and Funky would likely allow Funky at least limited access to K. Rool's technology and Kremling subordinates.
Neutral:
-Cranky: simply too old to care, Cranky's actual loyalties are difficult to ascertain. He berates Donkey, Diddy, and Dixie throughout the DKC games, but perhaps he was just being hard on them because he felt they weren't living up to their full potential. However, it's entirely possible he genuinely feels like DK is unfit for the throne. In this case, Cranky, ashamed of his own offspring, would likely support the idea of a stronger, more suitable leader, like Funky.