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.
If you're gonna just go trusting people, then why do you need your transaction on the block chain? The block chain is for when you don't trust anyone. You are arguing in favor of what amounts to security theater. People are worse off if they think simply having a private key is what makes their funds safe. Instead of them trusting a node to relay their petty transactions, they can just as well trust a bitcoin denominated bank to make a promise on their behalf. The banks can then settle balance differences in large chunks on a daily basis, thereby keeping the size of the block chain minimal. In this way, anybody can verify the process with an inexpensive node plugged into their home router. Whereas with your proposal, only a few wealthy people can verify the process despite everyone having access.
You have conceded that the common man will have to trust someone. Please stop with this nonsense that we must also make the block chain impossible for the common man to verify. It is not necessary to have both these results; only one is needed.