it's possible and depends on trading strategy,etc.. .after a specific amount of capital , the trading time frame and liquidity will be an issue .
a Eurex (successful ) trader claims in his interview that he had problem with liquidity in intraday trading because he trades big contracts .even the best traders have some years (even in row) drawdowns. the consistency is not only consistency in profits , whether it may be tolerating loss periods and continue game .what you mentioned is exactly what Warren Buffet did. he trades from age of 15 and used compound interest .after 70 years he is the richest.
No, it is not possible. Name one trader who has consistently doubled his/her money every year? Your mention of Warren Buffett is incorrect. His average annual return since the 70s is closer to 20% in excess of the T-bill rate, at least measured by shares of Berkshire Hathaway. Although, he once claimed he could guarantee a 50% return (I can't remember where I heard this though).
Maybe one way to end this debate would just be for someone claiming this to be possible to post audited trading results and prove it?