In the company I worked at, it depended on the seniority:
* CEO - He was in the open office but had his team of PA's and assistants around him, so if they didn't recognise you they would triage it first (and everyone knew not to just walk up in reality - open office at that scale means you can technically walk up to them and start talking but it doesn't mean that you should). The CEO in this particular company was a public figure too (i.e. the kind of CEO where reporters would follow them and would be recognised on the street), so again it's kinda like walking up to a celebrity in a cafe - you can but it's not always polite.
* Board/Exec Directors - They usually had 1 or 2 PA's sitting next to them but would be very approachable. Typically would have the desk against a wall to discourage disturbance slightly (i.e. it meant you had to walk past the PA desk). If you are in their department usually you could just walk over and chat. If you weren't in the department, the PA's would probably chat to you first and suggest speaking to one of the directors that reported into them first, although if they had done that already then they probably would either have a quick chat (director is in ear-shot anyway) or schedule a meeting if it needs a longer discussion.
* Non-Exec Directors - Were in the full open office, typically with one PA but they could be remote. You could walk up and start chatting openly.
For reference it was a company with over 100k employees, and 5 levels of hierarchy below director level. To be honest the whole setup worked really well, and I personally didn't feel like there was any barrier between management and everyone else.
* CEO - He was in the open office but had his team of PA's and assistants around him, so if they didn't recognise you they would triage it first (and everyone knew not to just walk up in reality - open office at that scale means you can technically walk up to them and start talking but it doesn't mean that you should). The CEO in this particular company was a public figure too (i.e. the kind of CEO where reporters would follow them and would be recognised on the street), so again it's kinda like walking up to a celebrity in a cafe - you can but it's not always polite.
* Board/Exec Directors - They usually had 1 or 2 PA's sitting next to them but would be very approachable. Typically would have the desk against a wall to discourage disturbance slightly (i.e. it meant you had to walk past the PA desk). If you are in their department usually you could just walk over and chat. If you weren't in the department, the PA's would probably chat to you first and suggest speaking to one of the directors that reported into them first, although if they had done that already then they probably would either have a quick chat (director is in ear-shot anyway) or schedule a meeting if it needs a longer discussion.
* Non-Exec Directors - Were in the full open office, typically with one PA but they could be remote. You could walk up and start chatting openly.
For reference it was a company with over 100k employees, and 5 levels of hierarchy below director level. To be honest the whole setup worked really well, and I personally didn't feel like there was any barrier between management and everyone else.