"To become the expert, you need more projects. They can be smaller, experimental, and even be isolated parts of a non-existent larger app."

This is so true. A lot of the 'experienced' people I've met in the industry with 10 or 15 years behind them have done nothing but their jobs in that time to practice their art, and their 'experience' is therefore of such low quality that an exceptionally good junior with a few hobby projects behind them can outclass them even in their own specialist area.