Modifying the_posts_pagination from within functions.php instead of template files

Is it possible to modify or give arguments for the original — in the functions.php file, not in theme
files — without wrapping it in a custom function?

No.

There are no hooks that allow modifying the arguments to this function. Wrapping it in your own function is the way to go. There’s nothing inherently smarter or superior or more smarter about using filters.