Hi Jan, that's a good question.
If you read Buffett's communications to Berkshire's shareholders, you realize that succession is something that he thinks about a lot. While the board of directors is doing everything they can to prepare for Buffett's passing away, they acknowledge that they'll never be able to completely replace Buffett. However, the good news is that the collection of companies that Buffett has amassed over the years won't suddenly lose their value.
Since Berkshire's price today is based on the value of those companies, any dip in Berkshire's share price will be an opportunity to buy. Note that this hasn't always been the case. In the past, Berkshire's share prices have sometimes traded above the value of the companies it holds. The difference between Berkshire's share price and the company values was explained away as the "Buffett premium". The premium essentially reflected investors' optimism that Berkshire will outperform in the future because of Buffett's magic touch. This premium is low, if it even exists today. In other words, you're not paying much at all for Buffett's unique skills when you buy Berkshire today.
As to why Buffett wants his wife to own index funds instead of Berkshire stock, that's because he has already committed to distribute all of his Berkshire shares to charity. That said, Buffett will leave some cash for his wife, and he did leave an instruction for her trustee to buy index funds. While I'm not 100% confident as to why, my guess is that he's worried that Berkshire could be overvalued by the time he passes away. Berkshire, like most other public companies, has gone through periods of overvaluation and undervaluation. His wife wouldn't be able to tell these periods apart, so he's opting for the safe choice.
As someone with some experience analyzing stocks, I feel more confident about gauging whether Berkshire is overvalue or undervalued, and I therefore feel confident about leaving Berkshire in the regular portfolios. If Berkshire's price becomes overvalued, I will take it out of the regular portfolios.
I hope this answers your question.