I am not 100% sure about the letter of the local codes or how strictly they are or aren't enforced, but my guess would be that they'd want to keep people from accumulating on the stairs for emergency egress considerations.
That said, a quick web search turned this photo up so they must not sweep through to keep folks moving all that often.
The last game I attended in Athens you were only allowed in certain areas of the stadium based on the location of your ticket. They actually had gated checkpoints set up on the concourse to insure your ticket allowed you access to the area. You had a very limited area where you could actually walk around. However, that was during the Crompton era, so it may have changed since then.