If we can have trusted places where we can download software without the fear of them being infected with viruses/malware then we can have trusted operators/nodes so that some users can use only a lightweight client without burdening them with a full node requirement.
Uhhh, there is no "full node requirement", there already exist a multitude of lightweight wallets that do not require you to d/l the block chain and there are thousands of trusted places these wallets look to, they're called full nodes; I think you're missing the point.