That one is pretty low. The 1 second warmup is extremely long.
I designed receivers for pager for many years. The best ones consumed 1 mA at 1 vdc fully on. You need a certain amount of current for dynamic range or there will be intermod issues with interferring signals.
The way to get power savings is by cycling strobing through signalling protocol. Example is wireless RF toll collection devices.
Cellphones, for example, have a complex warmup sequence that brings circuits up based on the warm up requirements of each circuit so at the end when signalling is needed they all are fully running. Cellphones have a tough dynamic range spec to meet so the best total ON current is about 20 mA from 3.8v battery. The cycling for 'sniffing' for incoming call is about 1 sec OFF and 5 or 10 msec ON times (for GSM).
TCXO, crystal oscillators, for example, take about 2 msecs to reach steady state because of the high Q resonators. Then you have PLL synthesizer to lock up. Our total warmup time including TCXO is about 2.5 msec but most of the ON current engages in last 200 usec of warmup sequence. Individual circuit designs must do decoupling in such a way not to take a long time to reach steady state.
The design needs to be fit to application. You might look into Zigbee devices. (802.15 protocol)