Face-to-face time is invaluable to me, but almost exclusively for brainstorming/working through difficult problems. But this can be a small minority of the week, and can happen opportunistically (when someone is available).
Maybe you should look into technologies like email that allows people to send messages that can be responded to when the person has the time.
Isn't it a given that very few companies actually are hiring the top 0.01%? Unless you really need the absolute world best, you're probably going to do fine hiring local people who can work together closely.
I (in North America) had to interact with a team member in Australia for a short project, and if either of us needed the other for something, we effectively had to find other work to do while waiting for the other to actually be awake and/or at their desk.
This would become far less efficient if we didn't all keep mostly the same hours.