I believe you will find these articles informative:
At room temperature (below the 31°C/87.8°F critical temperature) a CO2 bottle is to a practical extent self-regulating. This is not possible with simple compressed air. You would need a larger, stronger, heavier "high pressure air" bottle with a regulator (and its associated cost and complexity) to serve the same function.
This makes CO2 far more suited to a bicycle repair kit due to:
- small size
- low weight
- low cost
- reliability (simplicity)
This video of supercritical carbon dioxide provides an interesting window (both literal and figurative) into the phase behavior described in the articles above: