I am looking at door/window alarm designs, and they all use overcomplicated circuits with an always on switch, where the piezo is triggered when the switch is off.
If the switch was always off, it would be simpler, cheaper, and would consume 0 Watts at idle because the circuit would always be off unless triggered.
Why don't they use simple always off switches in between the piezo and the battery?
One of the design requirements is likely to be that the alarm should sound if the loop is cut by an intruder. By using NC switches the loop is continuously monitored.
With an NO scheme there is no simple way to detect someone cutting the loop. (It could be done by adding some resistance across each NO switch and periodically monitoring the total resistance of the parallel resistors but this would be more complex than the wiring diagram you have presented.)
So you can wire the whole lot in series. any switch opening - or anyone cutting the wire as Transistor says - will trigger the alarm.
This means running one wire from switch to switch round the house (and back to the alarm)
If you used normally open switches, you would need to wire them all in parallel - which means 2 wires running to each switch.