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?

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.

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.

Why shouldn't it? The shell is arguably the most convenient way to interact with your system's programs, seconded only by something like Perl. That level of interaction ought to mean you can write functions such as for common tasks. Or should I now have to use Perl for that?