Keeping a wallet online which does not perform staking is useless at least and detriment at most as that wallet does nothing but consumes the others network resources for nothing.
I like to push a theory to extremes to test its logic and by your statement, less online wallets is ok for the whole network, hmm so less and less.. now we have pushed to extreme and where did the network go?
To build a stable robust network you need as many nodes up and running 24/7 as you can get, PoS provides incentive to do this in the form of paying interest.
Yes and no. The network would be completely fine with just a single node online if it is reachable from everywhere. Yes, the bigger number of nodes helps to resist the DoS attack, but not staking nodes does nothing to secure the network from 51% attack.
There is 2462347.594957 TEK supply. How much of that is really protecting network? Ok, let's not be extreme. Say, that coin is distributed evenly and everyone is running the wallet 8 hours a day. Then it is 1/3 of all coins is protecting the network at time. But taking to account the will of many posters in this thread to get bigger reward by waiting for suitable difficulty I doubt that it exceeds 1/6 of all TEK in existence. Is this fair? Is this good for the coin?