this is John BG
1.- GFSK is not same as single tone
According to the CC1101 specs you refer to, the C1101 uses GFSK.
GFSK varies the varrier frequency, therefore the spectrum cannot be a delta.
Call it a 'shifting delta' but it cannot be same spectrum as just a tone.
2.- you want the carrier frequency to vary
ISM are crowded bands, the carrier has better chances to deliver if varying than if constant,
against jamming, interferrers, and any power level that neighbouring transmitters may radiate.
3.- not even ASK
You can still set modulation to MSK, OOK, or even ASK but even with ASK
Even with PKT_FORMAT[1:0] to Asynchronous mode, CRC disabled, Manchester disabled and PKTCTRL0 setting infinite packet length, PKTLEN is going to cut the packets to ensure syncing takes place.
This is done to avoid persistent propagation of errors along same packet that might generate uncertainty
to possibly overlap next packets.
4.- Temperature drifts, manufacturing tolerances
Such small and really low power devices may be subject to temperature drifts and manufacturing tolerances.
The packet header is needed at a high enough repetition to avoid transmitter and receiver missing frequency lock.
Hope it helps, John BG