TL:DR: No it's not possible to change the binding mode on the built-in controls.
x:Bind together with a few other markup extensions like x:Phase were all added to increase performance. Keep in mind that UWP applications can run on desktops, but also on the smallest IoT devices, so performance is key.
First of all, x:Bind is a compiled binding. During compilation the XAML is converted to strongly typed code behind, which is faster than the runtime object inspection used by {Binding}.
Second, it's optimized for performance by itself, using OneTime binding. OneWay and TwoWay bindings requires infrastructure to watch and push back changes.
The binding object can optionally be configured to observe changes in the value of the data source property and refresh itself based on those changes. It can also optionally be configured to push changes in its own value back to the source property.
In the past everything used to be OneWay with {Binding}, implying a small performance hit on every single field, even those that had to be bound only once (because why would you bother changing to OneTime if it just works). Now you're forced to think which fields should be update-able and thus use more resources.
More info on x:Bind on MSDN.