Not sure if fully remote is the best goal. What if a company is fully remote, except for ~10 employees in a city who request an office at the local downtown co-working space? That kind of flexibility would be ideal, IMO.
I think it is important that there is no headquarter. Some people having desks at the same co-working space is fine. All the executives in the same building means everyone else is at a satellite office.
People can choose to work together if they wish that's the whole point of fully remote.