you're right in terms of safety, not your keys not your coins
but some sites like freebitco.in and FTX are trsutable and there are high probability that you'll have no problem with them, as stated before.
If these sites allow us to export the private keys, then I don't have a problem with them. Otherwise I need to think about it. Keeping my hard earned coins for many months with a third party scares me, even if the site is quite trusted by the community. For me, it is a red flag. If I want to make a bet on 2024, I would only trust those sites where I can access the private keys to my coins.