Not if I want to actually affect the current shell environment.

For example:

    export MARKPATH=$HOME/.marks
    function jump {
        cd -P $MARKPATH/$1 2> /dev/null || (echo "No such mark: $1" && marks)
    }
    function mark {
        mkdir -p $MARKPATH; ln -s $(pwd) $MARKPATH/$1
    }
    function unmark {
        rm -i $MARKPATH/$1
    }
    function marks {
        ls -l $MARKPATH | sed 's/  / /g' | cut -d' ' -f9- && echo
    }
    _jump()
    {
        local cur=${COMP_WORDS[COMP_CWORD]}
        COMPREPLY=( $(compgen -W "$( ls $MARKPATH )" -- $cur) )
    }
    complete -F _jump jump

This would be much harder to do in a script.

I have a dozen of functions in my bashrc that are basically a bit more sophisticated aliases. Why would I want to load a whole interpreter to run them while bash can easily do that?

Shell functions are useful for much more than scripting. They are like aliases++, letting you add small commands to your shell where aliases don't quite cut it. They let you handle arguments, export environment variables, use conditionals, etc. I have 100 or so that I've added over the years. An interactive shell without functions would not cut it.