webpack 4 + babel 6 + ES Module and Script consumption

Question

I'm trying to create a library that could be used using one of following method:

import MyLibrary from 'mylibrary';
const instance = new Mylibrary();

and

<script src="mylibrary.js"></script>
<script>
    var instance = new MyLibrary();
</script>

To do this I have a very simple index.js which contains:

class MyLibrary {
    hello() {
        console.log('hello');
    }
}

export default MyLibrary;

And I installed webpack / webpack-cli / babel-core / babel-cli / babel-preset-env and babel-loader via npm. Then I created a webpack.config.js file with the following content:

const path = require('path')

module.exports = {
    entry: {
        MyLibrary: './src/index.js'
    },
    output: {
        path: path.resolve(__dirname, './dist'),
        filename: '[name].js',
        library: '[name]',
        libraryExport: 'default',
        libraryTarget: 'umd',
        umdNamedDefine: true
    },
    module: {
        rules: [
            {
                test: /\.js$/,
                exclude: /(node_modules|bower_components)/,
                use: {
                    loader: 'babel-loader',
                    options: {
                        presets: ['env']
                    }
                }
            }
        ]
    }
};

When I test it :

1.  <script src="MyLibrary.js"></script>
    <script>
        var instance = new MyLibrary();
        console.log(instance.hello());
    </script>
   

   Is working

2.  import MyLibrary from './MyLibrary.js';
    console.log(MyLibrary);
   

   I get the following error: Uncaught SyntaxError: The requested module './MyLibrary.js' does not provide an export named 'default'

If I remove the rule libraryExport: 'default'from my webpack config then:

1. I have to call my library like this: var instance = new MyLibrary.default();
2. I still having the same issue Uncaught SyntaxError: The requested module './MyLibrary.js' does not provide an export named 'default'

How can I do to get this work ?