I’d assume rainy UK would have softer runway surfaces for wet-weather performance.

Unlike car tires where people may switch them between climates/seasons, aircraft tires need to be fairly universal.

You're right of course, what I wondered was if the asphalt could become so soft that it loses consistency; some of it surely adheres to the tires, but what if it would do that by detaching from the runway? However, I'm certainly biased for having seen asphalt so softened by summer heat that I could leave my tracks just by walking on it.