If you need to leave, you can simply save the game. But I'm talking about other situations – when you need to step away for a minute and don't have time to save and message your opponent. For example, when you receive a phone call or are interrupted. In such moments, it's very frustrating, including the lack of the ability to pause the game.
In competitive games, people have always played with a chess clock and somehow manage without a pause during the game. There's a pause before making a move – that's quite enough.
Otherwise, if there are pauses everywhere, the essence of the chess clock is somewhat lost.