If you are adding wp_nav_menu() in different contexts it seems like you are techie / theme developer
I am not just thinking about me: I'm sure there are many non-developers out there that could find this feature useful.
wp_nav_menu() function allows you to call a custom walker (see reference). You can use it to achieve your task.
Walkers are for controlling HTML output. I use them all the time, but they seem highly overkill for the purposes described above, don't they?
If you need another menu - create it, it takes only few minutes in menu editor.
That may be your opinoin and/or way of going about it. However, I still think it would be nice to have the option to do it differently. THe argument is already included in other functions for which your same arguments could be applied. Yet, the argument is there. I am only asking to extend it to a very similar function.