Cold storage and transaction fees

I’ve heard that if you make multiple transfers from an exchange into your cold wallet, each transaction is subject to a (possibly heft)fee when you decide to sell, which means that in theory it’s better to stack a large amount in an exchange before transferring to cold storage…

But isn’t it risky holding such a large amount in an exchange, especially centralized exchanges like CB & RH? Is there a solution?

I’ve heard this is the case with Bitcoin but are other tokens subject to this? For the record my main holdings are Kaspa and Alien Base.