This is just an example of course. Succession can look differently and lead to very different results, depending on where exactly it is happening.

I'd also argue, that leaving your garden alone to let succession run its course is not neccessarily the ideal to strive for. Even simply speeding up the process to get to the final stage isn't.

Gardens are a very different sort of ecosystem from an extended woodlands area and there are many ways to use them for human recreation and as a habitat for many species, that even exceed the biodiversity of the potentially naturally occuring ecosystem.
A trimmed suburban lawn is just one of the worst options.