Unless your local security is worse than that of an exchange
Echoing this - for long term storage, they should be kept on a hardware wallet.
For long term storage, that sounds a terrible idea. Do you really want to trust your savings to $20 of electronic components that aren't designed to last more than a few years?
You should save the seed words somewhere as backup.
The wallets can be regenerated using your seed phrase. So your argument should really be, "Do you really want to trust a $0.02 piece of paper" :)
Exactly. The hardware wallet is pointless.
Yes. Put them in a offline wallet. Anything that is not on your machine is not yours.
Yes. Ideally, only money you should have on the exchange is stuff that you are moving around often. If you're trading you don't have a choice, but if you're just holding why not use a wallet you setup?
Get a hardware wallet. I like my Nano Ledger S, but there are others.