Apparently the issue was related to the Laravel layout page (app.blade.php). It already loaded jQuery when calling bootstrap. So in the php I don't need to load jQuery again.

So revision on app.blade.php:

    <!-- Scripts, remove defer from app.js, move selec2.min.js & select2.min.css here -->
    <script src="{{ asset('js/app.js') }}"></script>  
    <link href="https://cdnjs.cloudflare.com/ajax/libs/select2/4.0.3/css/select2.min.css" rel="stylesheet" />
    <script src="https://cdnjs.cloudflare.com/ajax/libs/select2/4.0.3/js/select2.min.js"></script>

...
...

<!- and adding this part -->  
@yield('scripts')

On the php side, changes on the Select2 are :

1. Right after onClick function, call select2('destroy') first
2. then clone the row contain select element
3. finally reenable Select2 on the last newly added element using select2().

@section('scripts')
<script>

$(document).ready(function () {
    $("#contents").children("td").children("select").select2();

    $(document).on('click', '#delRow', function(){
        if( $(this).closest('tr').is('tr:only-child') ) {
            alert('cannot delete last row');
        }
        else {
            $(this).closest('tr').remove();
        }

    });

    $("#addRow").click(function () {
        $("#contents").children("td").children("select").select2("destroy").end();

        // add <tr><td> directive first
        var newRow = '<tr id="contents"><td id="trx"><td> <i class="fas fa-minus-circle" id="delRow">';
        $(newRow).appendTo($("#treatmentlist"));

        // append select component on the last tr
        $('#treatmentlist tr:last').children("td:first-child").append(
            // clone the row and insert it in the DOM
            $("#contents").children("td").children("select").first().clone()
        );
        // enable Select2 on the last newly added element
        $('#treatmentlist tr:last').children("td").children("select").select2();
        // enable Select2 on the select elements
        $("#contents").children("td").children("select").select2();
    });
});
</script>
@endsection

While in the HTML, apply the changes as follow:

                <tbody id="treatmentlist">
                    <tr id="contents">
                        <td id="trx">
                            {{Form::select('treatments[]',$treatments, null, ['class' => 'form-control treatment', 'placeholder' => 'Select treatment' ])}}
                        </td>
                        <td>
                            <i class="fas fa-plus-circle" id='addRow'></td>
                        </td>
                    </tr>
                </tbody>