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.
I don't blame you for not trusting and totally understand your point
in the end it's a matter of risk/rewards
you don't have to keep all your coins on the same place (this wouldn't be so smarteven if you hold it on a hardware wallet inside a safe)
that said
it will be hard to find a website that let you bet on the elections in a trustless way,the closer I think we'll come to that is some smart contract on the ethereum chain, but you'd still have some degree of trust on the smart contract itself (which is usually auditable but not 100% free of the possibility of issues - like everything in life)