[Soft]

I don't think there are that many situations where it is actually productive to prevent user from selecting and copying text even if it's just part of the UI. To focus on your example, copying user interface text might be useful for users who are not sufficiently proficient in the language that the app/website is written in and would like to copy the text into something like Google Translate. This is especially a problem with many mobile apps that prevent selecting text.

[SAI_Peregrinus]

The worst bit is applications that prevent copying error messages, because they prevent copying all UI text. And then use complicated error codes. This makes searching for the error message/code excessively difficult!

[gridlockd]

If there's even one important situation where it is necessary to disable text selection, then disabling text selection must be supported.

I gave you several examples of these. The text for many UI elements isn't supposed to be selectable, because it interferes with user interaction.

Your off-chance example where somebody is trying to copy-paste the text for translation because the application is in a foreign language is subordinate to this.

Good UX is about choosing the right tradeoffs between functionality and usability.

[recursive]

I don't think it's that rare to have a UI element that's intended to be draggable and sometimes contains text.