Why would all pizeoelectric plugs spark when igniting just one gas stove burner?
Yes, it is a typical for the gas stovetops to light all of the burners even when only one is needed. Note that this applies to stovetops that do not have a standing pilot light. The oven often will have its own ignitor that operates independently of the stovetop.

The reason for this may be in order to reduce the complexity of the stovetop design. With all of the sparkers running in parallel, only one set of electronics is needed for all of the burners, instead of each one having its own electronics (or requiring additional relays). Stoves will often come with schematics showing their wiring, and you could consult these to see how your particular stove is designed.

Note that it is perfectly fine to spark already lit burners (though this will slightly reduce the lifespan of the electrode as it'll erode more quickly at high temperatures), and burners that are turned off (since there's no gas available, it'll have no effect).

There's also a bit of a a safety factor involved. If you have a failed ignitor (blocked with crud or broken), the plume of gas will be ignited by the other burner before it fills up more of the room, thereby creating a smaller fireball than it would have otherwise.