but also that is going to make things complicated.
lets assume you want to make a trade, you have to do all the signing,... and specially if you are keeping things in cold storage, that will be harder (time consuming) and time is sometimes important in trading with volatile prices.
the individual public keys used to form the multisig are empty of value. thus no need to 'coldstore' exactly.
because they are separate, that alone is a line of defense
because multisig involves dual signatures. an exchange via API can sign the tx(not on the front end) send the signed tx to the front end and then the front end sends the signed tx via api to the customers LN/multisig client.
thus the private key is not on the front end and transmission time is miliseconds (think how proxies work)
knowing the customer needs to sign too. the customer would refuse to sign if it noticed the destination of funds were going elsewhere. thus a hacker cant intercept. and also a hacker cannot change the destination after signing because the signature wont match the tx's new content.
lastly the customer just sends back a copy with their signature, thus also protecting their own private key by not having to use the privatekey within the exchange front end. but only on their own personal computer
also the first thing that came to my mind was confirmation time, but i don't think confirmation is necessary since it is a multisignature transaction and neither party can double spend, right?
because tx's are using real unspent funds and double signed it cant be double spend because funds cant move without both sides agreement.
and thus its no need to broadcast it to the network instantly. just holding a tx becomes like a bearer bond/promise/guarantee to pay.
i am not familiar enough with LN though, but from what i have read it seems like it can be good in this case as long as there aren't that much additional fees.
current LN concepts do have MANY 'penalties' so although you can re-sign thousands of tx's at an agreed lower fee per re-sign. LN hubs want to introduce other ways to make money, hold funds and revoke funds. so LN has some faults.
hense why im more interested in traditional multisig utility which has been built into bitcoin for along time now. but lets hope the LN concepts aimed at repaying blockstream investors is not so heavy handed with its penalties, otherwise LN will be impractical