While I suppose there isn’t any harm in sending an appeal letter, I think OP needs to move on. Admissions to schools in this country are so subjective. Your hard stats - grade, test scores, rankings - may only get you through the first round. Then it’s weighing EC’s, essays, LOR’s and other “factors”. Those are extremely subjective, and result in a landscape littered with highly qualified candidates scratching their heads about who got in and who didn’t and trying to speculate WHY. I really feel for you kids - it must be beyond frustrating.
Having a super strong resume increases your odds of getting into your desired schools, but there’s that keyword - “odds”. It is something of a gamble. When you go all in emotionally on one school, you are taking an incredible risk. While the high of getting in will feel absolutely amazing, the low of a rejection can crush a spirit like little else.
As a data point, I know a kid who got rejected by UC Santa Cruz, appealed, and got in, so it happens. I just don’t know about Berkeley. Especially since it was hard reject vs. being waitlisted.
So, OP, craft your letter if you feel you need to do everything you can, send it, and then get to work accepting - and embracing - another school. Even if you are one of the lucky, lucky few that they change their minds about, you probably wouldn’t hear until well after acceptances are due. In the meantime, you have to move on, physically and emotionally.