I'm sure you would agree with the fact that every single human being since Adam, has sinned every single day of their lives, and there's is no way they/we can stop sining every single day of our lives.You’re right that believers still sin, and you’re right that 1 John 3:9 and Romans 8:13 don’t teach perfection — but none of that proves sin is inevitable; the NT teaches that sin remains, not that sin must occur, and the break with sin’s dominion means the regenerate can obey in a way the unregenerate cannot; your model turns “ongoing battle” into “guaranteed defeat,” but Scripture frames it as remaining sin vs defeated sin, not “remaining sin vs inevitable sin”; the saved still fall, but they do not have to fall, because the Spirit makes real obedience genuinely possible.
I'm not suggesting that this is a good thing, to the contrary. I consider it a terrible reality, but it is the truth. You can duck and weave and dance around it, but it remains an ugly stain on humanity and it will remain until the end of time.
So, yes we all will sin every day for the rest of our lives. But those of us who are saved (Gods elect) can rejoice in the knowledge that all of our past, present and future sins are fully paid for by Christ so we won't be punished for them. That truly is good news for Gods elect.