DataGridView with DataGridTemplateColumns - Cannot create new rows

MainWindow.xaml

<Window x:Class="WpfApp1.MainWindow"
        xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"
        xmlns:x="http://schemas.microsoft.com/winfx/2006/xaml"
        xmlns:d="http://schemas.microsoft.com/expression/blend/2008"
        xmlns:mc="http://schemas.openxmlformats.org/markup-compatibility/2006"
        xmlns:local="clr-namespace:WpfApp1"
        mc:Ignorable="d"
        Title="MainWindow" Height="450" Width="800">

    <Window.DataContext>
        <local:ViewModel />
    </Window.DataContext>
        
    <DataGrid ItemsSource="{Binding Rows}" AutoGenerateColumns="False" CanUserAddRows="True" Margin="0,50,0,0">

        <DataGrid.Columns>
                
            <!-- Browse -->
            <DataGridTemplateColumn Header="Browse">
                <DataGridTemplateColumn.CellTemplate>
                    <DataTemplate>
                        <Button Command="{Binding Browse}" Content="..." Width="40" Margin="6,0,6,0" />
                    </DataTemplate>
                </DataGridTemplateColumn.CellTemplate>
            </DataGridTemplateColumn>
            
            <!-- Path -->
            <DataGridTemplateColumn Width="300" Header="Path" IsReadOnly="True">
                <DataGridTemplateColumn.CellTemplate>
                    <DataTemplate>
                        <TextBox Text="{Binding Path, Mode=OneWay}" />
                    </DataTemplate>
                </DataGridTemplateColumn.CellTemplate>
            </DataGridTemplateColumn>
                
            <!-- Slider -->
            <DataGridTemplateColumn Width="100" Header="Slider">
                <DataGridTemplateColumn.CellTemplate>
                    <DataTemplate>
                        <Slider Value="{Binding Value, Mode=TwoWay, UpdateSourceTrigger=PropertyChanged}" Minimum="1" Maximum="50" Margin="6,0,6,0" />
                    </DataTemplate>
                </DataGridTemplateColumn.CellTemplate>
            </DataGridTemplateColumn>

            <!-- Slider's value -->
            <DataGridTextColumn Binding="{Binding Value}" Header="Value" IsReadOnly="True" />

        </DataGrid.Columns>
    </DataGrid>

</Window>

MainWindow.xaml.cs

using System;
using System.Collections.Generic;
using System.Collections.ObjectModel;
using System.Globalization;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
using System.Windows;
using System.Windows.Controls;
using System.Windows.Data;
using System.Windows.Documents;
using System.Windows.Input;
using System.Windows.Media;
using System.Windows.Media.Imaging;
using System.Windows.Navigation;
using System.Windows.Shapes;

using PropertyChanged;

namespace WpfApp1
{
    /// <summary>
    /// Interaction logic for MainWindow.xaml
    /// </summary>
    public partial class MainWindow : Window
    {
    }

    public class RelayCommand : ICommand
    {
        public Action CallBack { get; set; }
        public Predicate<object> Enable { get; set; }

        public event EventHandler CanExecuteChanged
        {
            add { CommandManager.RequerySuggested += value; }
            remove { CommandManager.RequerySuggested -= value; }
        }

        public bool CanExecute(object parameter)
        {
            return Enable == null ? true : Enable(parameter);
        }

        public void Execute(object parameter = null)
        {
            CallBack();
        }
    }


    [AddINotifyPropertyChangedInterface]
    public class ViewModel
    {
        public ObservableCollection<Row> Rows { get; private set; }

        public ViewModel()
        {
            Rows = new ObservableCollection<Row>();
            //Rows.Add(new Row());  // Uncomment this line and the binding works
        }
    }

    [AddINotifyPropertyChangedInterface]
    public class Row
    {
        public RelayCommand Browse { get; private set; }
        public string Path { get; private set; }
        public double Value { get; set; }

        public Row()
        {
            Browse = new RelayCommand();
            Browse.CallBack = BrowseFile;
        }

        private void BrowseFile()
        {
            Path = System.IO.Path.GetRandomFileName();  // Some random string.
        }
    }
}