Then you're up shit creek.

Very few wallets control your coins these days, and any that do should be avoided completely.

As for places like Coinbase and Xapo you can sugarcoat it all you want, but no matter what the arrangement some other bastard has full control over your money and are permitting you access to it.

Of course places that well known and capitalised are not going to do a runner but there's no predicting what the future holds. If the American government can confiscate everyone's gold, which would've been a fully manual process all those years ago, imagine how much easier it would be with millions of people all herded into a couple of services.