Can't keep your funds in cold storage, which creates a real security risk.
Wallet must be open to receive the funds
if you think about these statements you most probably won't make them.
a cold storage is always a way to
store your coins not to spend them. for example think of paper wallet, you are not making a paper wallet to spend from it.
for that you have a "hot wallet" which you have funds easily accessible to you. the use of lightning network and the open channels,... can be exactly this. you don't go in your cold storage to pay for coffee, you use the hot wallet and that is where LN comes in. even if you lose the funds because of the security risks it will be your hot wallet funds which are always small amounts like $20 in them.
May not be a channel open for the transaction to reach your wallet.
i am not sure but i think the process only takes seconds to complete.
keeping a channel open is only for when you want to continue being involved with the network not just when you want to receive funds.
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.
first of all same goes with bitcoin and also cash. specially cash if you have any of it, there is always a good chance that those funds were involved in something illegal.
secondly LN uses onion routing as far as i know which makes it impossible to know who send what and where and from where they are receiving things.