Nothing, I trust a personal wallet more than storing crypto assets on any exchange.
If it's not a non-custodial wallet, maybe you shouldn't trust it 100%. During this time quite a lot of people use trustwallet or any other wallet that is not open source for their online storage needs, it is also personal wallet, but the security is also at risk. Having an offline wallet or a hardware wallet are good options but you can also use an open source online wallet for a limited amount of funds.