Makes very little sense for those who know what they're doing.
If you have LeBron James on your team, don't take him out of the game just to make room for someone else. An investment portfolio is no different. It's crazy to put money into your 20th choice, rather than your first choice.
Buffett has embraced that approach at Berkshire. Its five biggest holdings — Apple, Bank of America, Coca-Cola, American Express, and Kraft Heinz — account for more than 75% of its roughly $200 billion stock portfolio.
In one of his talks to his shareholders: “99% of people who invest should be extensively diversified and not trade, so that leaves them to an index fund type of investment, a decision with very low cost. Unless they want to bring an intensity to the game and start evaluating businesses. But once you are in the business of evaluating and you are willing to bring the effort and tensity and time to get that job done then diversification is a terrible mistake! If you can identify six wonderful businesses that is all of a diversification you need. Very few people got rich on their 7th best idea but a lot of people got rich on their best idea.”
..and in another one: “Big opportunities in life have to be ceased. We don’t do very many things but when we get the chance to do something that’s right and big, we’ve gotta do it. To do it in a small scale is almost as big a mistake as not doing it at all. You ‘ve got to grab them when they come. You re not gonna get 500 great opportunities.”
Of course, selecting stocks or even asset classes for a concentrated portfolio requires a lot of analysis and attention. An investor with a concentrated portfolio needs to put the work in and must know as much as possible about their investments. They should be reading industry reports, studying financials and tracking the business environment carefully.
"The determining trait of the enterprising investor is his willingness to devote time and care to the selection of securities that are both sound and more attractive than the average," Buffett's mentor, Benjamin Graham wrote in his seminal tome The Intelligent Investor.
Obviously, this method of investing is not for the "set it and forget it" type of investor. Those unwilling to put the work in should probably stick to index funds.
If you have a financial advisor or money manager who is a fiduciary (and you should), they will most likely be unable to set up a concentrated portfolio, so you'll have to do it yourself. Fiduciaries are legally required to act in what they believe to be in the best interest of their clients. You'd be hard-pressed to find one who would set up a highly concentrated portfolio since it runs counter to conventional thinking.
There is no correct answer to this question. Some investors might be happier with a concentrated portfolio. Others may not be able to tolerate the volatility.
If you are willing to put the work in, however, you may be richly rewarded for your endeavor. Better to be like the wise man: put your eggs in one basket and WATCH THAT BASKET!