How many full nodes do we need? Is it just "more" or do you have a quantified target number/percentage?
I would guess not as many as today. This might be solution looking for a problem. I would first ask if DNS, NTP, TOR are at risk of denial of service attacks with current numbers of nodes. DNS has 400 root servers, NTP pool has 3500 servers, TOR status page listed 5000 nodes cached.
Bitcoin needs redundant amount of nodes in each legal region it wants to operate in. Maybe 3000 really is enough. In the future blockchain size will cut full nodes to similar numbers that we have serious miners.
PoS also acted as cheap block creation tool. I think it's a worthwhile idea to explore even if node security isn't the best motivation.
It's very unlikely that you'll see this type of proposal included within bitcoin, but there are alt-currencies planning the first few tentative steps towards your idea.
Yes I'm aware. I was making the leap to improving bitcoin itself even if it seems unpopular. The motivation wasn't inflation, free interest or newer coins.