That's not quite true with CSMA-CA. The minimum medium aquisition time is effectively a constant, no matter the bandwidth. Wider channels mean you've got the same duration of deadtime across more channel bandwidth for each transmission. In fact it's worse than that - wider channels mean more senders compete during each medium aquisition, so collisions are more likely, further reducing capacity. The use of AMPDUs in 802.11n (and later) goes some way to mitigating this, but our measurements show it doesn't do a great job in practice with many workloads. In the end, if things are really congested, you'll get more total capacity with narrow channels, at the expense of not being able to burst at high bitrates when things are quiet.
Well, if you want to argue from a theoretical point of view, the fundamental constant determining the CSMA-CA slot length is the speed of light within reception range, which is effectively constant, and the requirement to demodulate the carrier signal to perform carrier sense, which also has a fundamental time constant related to carrier frequency. Of course DIFS in 802.11 is much larger than that fundamental limit, because carrier sense needs to implemented in real low-power hardware.
