In my opinion, this way of connecting is very complicated and unjustified. If I needed a lot of buttons I would use several 74HC595 registers connected in series and 1 Arduino pin as input. Thus, each added 74HC595 adds 8 buttons and the number of required Arduino pins remains the same - 3 for registers control and 1 for reading a pressed button, ie. total 4. Or I would use an IR remote control connected with a cable and in this case I will need only 1 pin - with 2 wires from the IR diode to 1 pin of the Arduino and ground connection.