This gets repeated over and over, but people just don't listen until it is too late. Keeping money on an exchange is the antithesis of why crypto-currencies were invented in the first place.
Most people getting into cryptocurrency at this point aren't going to be able to spin up a secure debian box, download and run zcashd, run it until it syncs with the network, construct a transparent address, round-trip a test portion of their exchange funds through the address, park their on-exchange zcash there, and put the wallet.dat file somewhere secure from hacking or destruction. But my understanding is that Ledger can handle transparent zcash transactions, which potentially massively simplifies matters.
Or someone just forces you to give up the info?
As someone said earlier in this thread - Hardware wallets are simply another computer that stores your private key. There is nothing inherently different about its "Hardware".
You can import that seed phrase into any number of wallet programs if you lose your hardware wallet.
Their absolutely is. A hardware wallet can take unsigned transactions and sign them internally, and output a signed transaction. Your private key never leaves the hardware wallet.
Compare this to signing a transaction with a private key on a computer. Your computer can have spyware that can snoop on the key and steal your coins.
The hardware wallet has a burned ROM with a firmware that is signed and verified every time you use it.
So could a hardware wallet. [0]
[0] https://en.bitcoin.it/wiki/Hardware_wallet - see under "Security Risks", both the "compromised production process" and "compromised shipping process" items are places where this could occur.
I've started trading in this space with a modest amount, but as I plan to increase some of my investments I am definitely considering purchasing a wallet.
I would sleep better if I knew my coins were not held within the exchange.