Second, if the only interviews you get are "whiteboard coding", and the only rejection is "not a cultural fit" you may not be interviewing in the right place. Not all places want you to be a 10x engineer who's gonna work 80 hours a week.
I'm surprised you encountered this behavior in larger companies. You said you got introductions from your friends, I assumed you interviewed there. I would try to get more constructive feedback through your friends to really know what's going on.