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.
Anyone coming with that argument using exchanges as wallet, not running a full-node and having cold storage is a huge hypocrite. That's like 99.99% of people.
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.
Same as above.
You really think everyone is going to run a full node just so they can use lightening network & secure there funds, your dreaming. The simplest route is the most successful and there is nothing simple about that at all. The whole concept is to make it easy, cheap and fast to send BTC and so that those 99.99% of people you refer to, can use it . Your delusional!