Unfortunately, there is no way to scale anywhere notable on-chain, it's just not realistic, unless of course, you don't mind bitcoin being hosted in centralized hubs, which would kill the point of bitcoin.
Sorry to harp on about this, but that isn't strictly true. Halving the block generation time, and adjusting the mining rewards, doesn't seem to be a major task. Of course, that assumes consensus amongst the byzantine generals.
In order for what pereira said to be untrue, your statement would need to be true. But your statement's wrong.
Everything you said was correct, in isolation. Except that none of what you said makes Bitcoin scalable. Because halving the block interval isn't going to be feasible more than once, and the majority technical opinion is that even cutting the 10 minute target carries too much risk from constant chain-reorgs.
I'm absolutely fine with people finding alternative scaling solutions, but they have to be actual alternatives, not just a pleasant thought-experiment that lasts 5 minutes.