During WWII, I'd be surprised if there was much that absolutely had to operate off concrete....perhaps the B29.
It's really all about the loading of the tires. I don't know what the number is, but there comes a point at which the amount of weight vs the area of the tyre goes high enough that unprepared surfaces can no longer provide the strength needed. But, big tyres, that spread the load, also take up a lot of space and weight. Like everything, a trade off.
The A4G tyre loading was so high that it needed a dispensation to be allowed to operate into Mascot! They were tiny...and ran at 440 psi.
Now, anything from the fighter or naval world will be unable to, but I'd expect most tactical transports would be quite happy.
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