Another pitch to let the steward come in and do their job. You'll enjoy the cruise more if you do.
We've never had any security issues with our stewards. We put valuables (electronics, wallets, passports, etc) in the safe and they stay there unless we need them. Everything else we try to put in a drawer, the closet, on the shelves, or in the suitcases under the bed so the steward doesn't have to clean up around our stuff.
I asked one of our stewards why they left the cabin door open when inside. He said it was so they had quicker access to their carts, which are left outside the door; to let guests know someone is in their room if they return; and for the steward's personal security since it is harder to be accused of theft, assault, etc if the door is left open for others to see in and hear. They are not supposed to leave the room open and unattended, and I've seen more than one close the cabin door to do something, then return to and reopen it to finish what they were doing.
I make a point of meeting our steward on the first day, and I make sure I greet them whenever I see them. If I see them in the passageway and they are carrying something or pushing their cart, I step out of the way to let them through, usually saying something to them about they are working but I'm on vacation so I'm in no hurry. I let ours know we drink wine in the room so ask they replace our wine glasses each day (the first day I get them from one of the lounges/bars). Invariably, they leave us a bucket of ice as well.
I spend a lot of time on our veranda, especially on sea days. If the steward comes in, I just let them know I'm on the veranda and they can do whatever they need to do. Mine have always knocked before entering and usually they will not enter if you're in the room, but excuse themselves to return later. They have also followed the open/closed door procedures I mentioned above, even if I'm on the veranda.
About the only time we put out the DND sign during the day is if we're changing clothes. I put it on the door on sea day mornings as DW likes to sleep in. One evening DW became ill during dinner so after putting her to bed, I put out the sign and returned to finish my meal (my servers even brought a fresh plate for me).
The cabins have sofa beds that are quite comfortable for napping. Both my kids and I have used it at one time or another for that purpose.