Later on the site it turned out that the minimum need is 0.002 per wallet. Why do you say 0.003 is the minimum?
Either he got confused or added the channel opening transaction fee.
Why is that? After all, LN is designed to increase the speed and reduce commissions on transfers
You are missing one thing. Channels are supposed to be used more than once. Most people use the Lightning Network for small transactions which would be cost-ineffective to send via an on-chain transaction. Larger payments are also becoming feasible thanks to increasing network's liquidity and multi-path payments.