Hi Djulia,
So you were referring to the menu suffix icon and not the prefix.
No, I don't think we need a field in the section editor for the suffix icon because I think it will not be used that much.
We can use the plugin filter to add/change the suffix icon for now unless many people asked for a field to set it.
And right, you can hide it using CSS or update it to change to other icon using the plugin filter.
Cheers,
Daryl Maximo
PHP Programmer - interactivetools.com