In short, culture is the internalized, repeatable way of doing things in a company. It's how companies like Pixar, Google, and Amazon scale while still maintaining their original, early identity.
Culture is how identity scales.
A culture is developed by observation and emulation as much as by intention. There's always someone watching, and that's the opportunity for leaders to scale values and priorities: by showing by example why those values and priorities are right for the goal of the organization. Every time there's unexpected problems, bad results, hard conversations to be had, or tough decisions to be made, it's an opportunity to build a culture that deals with those situations the right way.
Incidentally, this is why good leadership is not a result of good acting or planned manufacturing; sooner or later, the true identity colours of those at the top arises, and those are the values and priorities the organization will adopt.
The scariest part is that it doesn't take long for a culture to pass the point of no return. To quote "Thiel's Law": a startup messed up at its foundation cannot be fixed. It requires a superhuman effort to assess the past objectively, and acknowledge that the important decisions taken were wrong, whether that was defining the goal of the organization, the assumptions of the business model, or the team members' responsibilities (specially hard in this case, IMO).
If the leadership's example is weak, it creates a weak culture. ¿What is a weak culture? A group of individualistic identities. No priorities have been agreed on, no values have been transferred. There can be effective collaboration, but not scalability.
Which takes me to the biggest tradeoff of remote work; since leadership's behaviour cannot be observed by remote workers, because there's no shared space during the unexpected moments of business life, they cannot become vehicles of the identity of the organization. They cannot learn how to scale the organization's creativity, discipline, resilience, maturity, honesty, empathy, charisma, dedication to excellence, and all the other things that make a large, successful organization.
Remote workers can only execute on what is very clearly defined and expected by their managers. And only a very arrogant leadership would claim to know how to transfer things like discipline and charisma through an SOP, instead than by showing it.