Eliminating a Supreme Kai breaks the equilibrium of a universe in Dragon Ball Super. When a universe’s Supreme Kai dies, It’s God of Destruction dies as well, which will make the expansion of the universe stagnant, and open for destruction.
The Supreme Kai’s job is to create, and shape the universe. They oversee civilizations, and make sure the ratio between creation and destruction is somewhat equal. They are also in charge of taking down multi-galaxy level threats and other issues in the universe, and they watch over the time rings as well, which makes them the guardians of time in that case. Without them, there would be no divine force stopping multi-galaxy threats like Buu from causing mass destruction and disrupting the equilibrium unless that universe has it’s own version of the Pride Troopers or the Z fighters, but then again there is always a possibility that the enemy could overwhelm them and rule over the universe.
The God of Destruction’s obligation is to destroy civilizations that are deemed as failures, in order to get rid of the “clutter” in the universe and maintain a positive mortal ranking. Competent Gods of Destruction, who don’t destroy on a whim, destroy based on food like Beerus does, or don’t show pity like Sidra does, are the driving force to maintaining a healthy and thriving universe that isn’t facing erasure by Zeno. Without a competent GoD, or even a incompetent GoD, there is no safety net for the universe, and all of the destruction will be unorganized and detrimental. Also, there is no strong figure to stop an enemy that becomes universal level besides Zeno and the Angels themselves, who are often indifferent when it comes to mortal affairs, and only show up when they’re directly summoned, i.e Goku summoning Zeno. In addition, the ranking will go down because there will be low civilizations attacking high civilizations, like Saiyans killing off the Truffle race, which had a higher civilization than them and had way more potential (As a race, not as warriors). So the chances of the universal getting erased are increased, and the universe will deteriorate.
In short, eliminating a supreme Kai breaks the universe, and opens it up to serious threats, like Goku Black, or someone even stronger than that. Also, it increases the chances of those threats taking over the universe because the Supreme Kai’s usually provide help with threats like these. For instance, if it wasn’t for The Supreme Kai warning the Z Fighters about Buu, he would of been resurrected and nobody would be able to stop him; SSJ3 Goku would probably briefly overpower him, but in the long run he’d lose due to Buu’s regeneration. It’s an interesting thing to think about, and I myself, never truly realized how bad it was for a Supreme Kai to die until I started writing this answer although I have already known it would be bad based off the Goku Black arc.