Customer is either worried your company is too young/unstable or it's the standard procedure. If your company goes bankrupt then it's indeed unclear to me who owns the source code, the escrow contract might cover that.

Increase the price, double it, that's a very custom request for you.

We did it 6 years ago with a big enterprise customer. The escrow company got read access to one git repository (custom development outside our usual offering). I think the other option was to send them a DVD with the code. Customer paid for the escrow. A year later they either forgot or cancelled, we never had to update our code. Monetary the customer contract value was worth the trouble. We never had another escrow request.