+4dBu is 3.472 V peak to peak. You’d need 3 batteries to hit full line level, before you even get into the 0.7v silicon junction losses.

Remember that you’re making an AC signal from a DC power supply. The output is centered at half the battery voltage. It’s exactly the same as a class A amplifier.

People already use 9V for their pedals too.

Voltage. AA and AAA are 1.5 volts. A 9volt has essentially 6 AAAA batteries in them ran together in series to provide 9-volts. It’s a common standard, and has the snap terminals which is good for things that are moving around instead of a spring loaded compartment.