Mate, I disagree with what you said about buying bitcoin with a gas fee on a centralized exchange; bitcoin does not have a gas fee if you want to buy it on a centralized exchange. The only time you will pay a gas fee is when you want to withdraw your bitcoin from the centralized exchange to your noncustodial wallet or when you want to send bitcoin to a family member from your noncustodial wallet.
In what exchange you buy Bitcoin without any fees? As far as I know, there is a trading fees for any coins we buy on centralized exchanges. It doesn't make sense if we buy Bitcoin with 0 fee. I have joined many centralized exchanges, I didn't find a centralized exchange that give 0 fee for buying Bitcoin. I think you need to check again the information related to trading fees on the exchange!! 
Sure, if we want to withdraw the Bitcoin, we need to pay some transfer fees. It is not only Bitcoin, other coins must also have some fees when we want to send them to certain wallets.