From my perspective disabling text selection by default on mobile is a good approach.
In almost all mobile web applications/frameworks and native mobile applications, by default you will be not able to select text, but only in some special use cases when it is required.
In other scenarios when drag and drop is supported or where is a high risk that text may be selected accidentally, e.g: buttons, the text should not be selectable.
It really depends on what content you're displaying. If it's designed like an application more than a website, it would be better to disable text selection. But in most cases you're displaying some text which user might want to copy and save, send to a friend etc. In that case, the UX degrades. In my opinion, best way would be to create a css class (you're talking about web design so I'm 100% that css will be involved) and apply it to all elements that should not be selectable, like you've mentioned. This is also good practice for standard web design, not only mobile.
While I will concede that certain aspects of the interface should not be selectable, and that having portions of the interface be selectable would most likely degrade the user experience, making all content non-selectable isn't the correct choice.
A good example would be any application with contact information. While copying and pasting may not be used by the majority of your users, having the option available shouldn't negatively impact the user experience. Sharing information between your application and other mediums, whether it be email, SMS, or even the phone application, shouldn't be hindered.
We see these patterns in most applications - for example, the iPhone's SMS app allows the user to copy the content of the SMS, but not interface elements.
Removing a functionality should be done only if it broke the application main usage.
Most of the times it's not your application job to restrict user interaction. If your user want to search a word on dictionary, find the address on a map, phone to the number displayed, find user's advice on a product, or even tweet an extract of your site/comment/score to game he likes, you will generate only frustration if he can't do what he wants. It may even push him to another site/application.
Copy/Paste between applications is one of the few feature which change computer usage. It was the first time applications from different company were able to communicate only by user will.
