Returning to the OP's initial post, I see that he said
"sat with my bag under the seat in front of me because the bins were full." I'm not trying to be horrible but, that's what that space is for. As for what passenger's carry with them when they board, that is to subject to 1. Airline Policy, 2. Check-in administration, which should reflect the airline's policy, 3. Cabin Crew actions on boarding and lastly 4. Support from the company which should back the cabin crew when they make decisions whenever there is an excess of cabin baggage. For me the easiest method is to place excess cabin baggage in the hold. I will state politely that the bags will be going in the hold but also there will be no discussions about it. At the same time, I am also acutely aware as to who pays my wages.
As for the question:
If we design, say a wardrobe, for crew luggage (which already exists on some types) how long is it before passengers want that space too?
Answer: As soon as it is installed. And it is up to the crew to offer/deny the space.
Finally, it is up to us as crew to let our respective companies know how well their baggage policies are working and what they have to do improve them. We also have to take action when the check-in and gate staff allow excess baggage through. I'll make a call immediately we have excess baggage and make sure any delay is down to the handling agent. But at the same time, I'll always back them when they stick to our ground handling manual. Unfortunately, far too many employees and agents attempt to place sticking plasters on a broken system - one which in many cases, is in dire need of radical redesign.