I am starting to wonder whether lightening network really can do what they say.

There are so many negatives to prevent it from working:

Can't keep your funds in cold storage, which creates a real security risk.
Wallet must be open to receive the funds
May not be a channel open for the transaction to reach your wallet.

Those are just some, but probably the biggest concern is that if you are using your wallet as a node/hub for the funds to hop through then there is a good
chance that you could be seen to be involved in the transfer of money and depending on the jurisdiction you reside in, may be subject to anti-money laundering laws that require you to KYC the people sending and receiving the funds or even worse comply with anti terrorism laws.

Governments all around the world are working on ways to legislate the crypto environment and l can't see them letting us use our wallets for the transfer of money and not knowing from who to who!

If they really want Bitcoin to be cheaper and faster then they should just implement Segwit2x