I carry CO2 on the road and a pump off. The only time I’ve had to cycle home on a half inflated tube after a puncture was due to a broken pump while MTBing ironically.
On my road bike I have a tiny saddle pack with 2x CO2 cyclinders, inflator, tyre levers, patches, inner tube, multitool. All packed in very tightly so they don’t rattle (very important).
I don’t see it as too much of a risk, I can fill 3 punctures with 2 cyclinders and with CO2 you can get a good presure after the first puncture so a second is less likely than with a tiny mini pump that can only get to 75psi.
Taking a pump on road is always a compromise between bulk, looks and comfort.
Pump in saddle bag means a giant saddle bag and/or ineffective pump
Pump on frame looks naff
Pump in pocked is uncomfortanble, looks naff and might hurt if you crash.
(I have obviously now angered the puncture fairies so will be taking a pump with me on my next ride!)