Today we are not reliant on third parties to transact on the Bitcoin blockchain directly and cheaply.
Your lack a lot of knowledge. The majority of people rely on third parties today. Anyone who does not use a full node (e.g. online wallets) relies on a third party. Online wallets are the worst though, users don't even have access to any private keys. Increasing the block size limit makes it harder not to rely on third parties.
This would also take transaction fees away from the miners.
No.
I have nothing against the lighting network, even if it ends up being highly centralized.
You do.
However it should not be regarded as a replacement for the every day transactions we do on the Bitcoin blockchain today.
Creating a second layer does not replace anything, it supplements the system. Should I tell you how the internet functions on 7 layers and probably never would properly function on 1?
I suppose if we moved most of the transactions off chain that would be true.
There's no correlation between his statement and off-chain transactions.
However if we do scale Bitcoin by increasing the blocksize I see the mining power of the network continue to grow as its value grows providing greater security for the entire network.
Or the network experiences more centralization, higher orphan rates and possibly an attack. Stop looking at the 'best case' scenarios, we need to be prepared for the worst ones deal with tricky situations.