Why does the reset button on html forms not reset hidden fields?

FWIW, I think I can put together the full story from the answers and comments.

Usage rationale: The clear button is intended for clearing user input, and since hidden inputs are not directly accessible by the user, it doesn't make sense to allow the user to reset the hidden input's value.

Documentation and behavior: The bug report that AR pointed out is explicit about what is happening: The hidden field's value's mode is default, as is intended in the specs.
Particularly, this means that changing the value (as in the sample code in the question) changes the default value, and the reset button resets input fields to the default value, hence there is no change.
The behavior for the text input is different (even though its value is also changed programmatically) because its value's mode is not default but value, which means that there is a distinction between the default value of the input and the current value.

The user can't see or modify the hidden field, therefore it wouldn't make any sense for them to be able to clear it by pressing a button.