Maybe 300mA order of magnitude is more common than 3A, but it's not inconceivable. Lots of designs wake up, burst some RF data at a few hundred mA transceiver load for a few tens of microseconds, then go back to sleep for another few seconds. There are some long-interval scientific instruments that need high-speed ADCs or DACs on battery power in remote locations, which might get into higher current than a few hundred mA. Some deep space crafts can sleep at very low power and run their transmitters at comparable currents. It's very situational.

Older cell phone standards used to burst to about 2.3A upon initial connection to a tower before the tower told the handset to dial it back. I don't know about modern cell phone standards.