The only liquid cooled airliners were a Few Canadian and British plane using Merlins. At the time the British (including the Commonwealth) had one heck of a trade deficit problem and foreign (meaning US) engines simple could not be afforded. That left the Merlin, Griffon, Sabre, Hercules and Centaurus engines. The Sabre and Griffon found no takers at all in the commercial field and Rolls, by expending a fair amount of effort and trading a bit on the Merlin reputation did make the above mentioned sales. Commercial Hercules ( even licence built in France) and Centaurus engines filled the British commercial aircraft until the jet and turbo prop.
The Americans, for a variety of reasons, dominated the post war commercial aircraft market and so did American engines, which after the Allison stopped production, meant air cooled radials.
One less system to fool with and maintain and with acceptably low operating costs ( and airline owners are a hard headed tight fisted bunch) the air cooled radial did the job.
The other factor was the incredibly low price of avgas in those days. I suspect that if ICE were still used today for airliners, that they would all be liquid cooled because of the lower specific consumption.