You think that most people should rely on off chain solutions? Needing third parties in order to transact in Bitcoin defeats part of the purpose. We should be able to use the Bitcoin Blockchain directly, off chain solutions do not truly increase the throughput of the Bitcoin blockchain.
I think icebreaker missed that part:
What is needed is an electronic payment system based on cryptographic proof instead of trust,
allowing any two willing parties to transact directly with each other without the need for a trusted
third party.
The only way to use Bitcoin without relying on a third party is to run a full node. How else do you propagate your transactions privately.