Looking at this picture of Jonathan Slinger as Richard II you are struck by the richness of the image with the stairs doubling as a throne for the king. As Richard’s status declined Jonathan took his seat further down the staircase.
Then as now height symbolizes power and status so that the figure of the king could be seated high up on the stage. This would also allow a good view a lovely costume to the whole audience. The simple portable steps arrangement was easily compatible with Shakespeare’s bring on/take off props aesthetic although the structure was probably more throne like in Shakespeare’s theatre.
A structure simple enough to be pushed onto the stage through the discovery space – in-between the entrance doors in the picture here – would have been simple enough to use. It would probably have looked a bit like a throne on a plinth and would have easily served to elevate Richard above the others.