This advice worked for me and several of my long term colleagues across decades of career experience. We’re all introverts so this is a big deal for us.
I suspect you are giving up too easily.
Modern whiteboard interviews are not decades old. I never had any issue until the last 5 years or so. Tech interviews are testing for presentation skills and brainstorming skills, and placing a lot of weight on those alone. If that is what the job is like then I don't want it.
If your idea of best practices is copying (as best you can) someone else then I'm not a good fit for your company. In my view, its your loss and not mine - you missed an opportunity because you are not creative enough to see any other workable process.
I passed the last crap whiteboard interview I went to, even the question that no one else had gotten right previously (so they say). Didn't get the job, over-qualified - they wanted someone cheaper really. It is not about giving up too soon, its about doing something I dislike, and that has nothing to do with the day-to-day work, over-and-over.
Can't tell you how many companies I interviewed with that simply take their entire process from others. We interview like X, we group teams/squads like Y, we do our agile process like Z. I don't want to work for your wannabe something else organization, get a clue.