There are several things at play in this question.
First, leaders need to understand their role in growing and developing their employees' skills and talent, and being comfortable sending them off to the next role. Too often, leaders hide their top performers, fearing a hit to the department if they leave. This really talks to the culture you've built in your organization - much as you are describing in those companies you list - where growth is the norm, and employees are encouraged to learn and develop for future roles.
A collaborative talent management process driven by a technology platform can be very helpful, but only if the culture supports and, in fact, promotes growth. One element of a talent management program that has served my organizations well is the assignment of talent to cross-functional project teams. It gets the employee out of the daily routine, exposes them to others in leadership roles, and tests their resilience to change.
I caution you though, about looking at filling positions exclusively from within. I have found that over time organically grown leadership teams become myopic, and struggle with challenging their own status quo. A realistic infusion of talent from other companies and even other industries can disrupt this tendency.
In terms of growing leaders, I go back to the 80's when organizations rotated talent through line and staff positions in order to expose them to the whole business, rather than a silo. We seem to have sacrificed that process because everyone is so busy, but it is a phenomenal way to not only develop talent, but build collaboration.