Zulu,
Aircraft tires are required to withstand landing speeds of 250mph as well as static and dynamic loads of 22 and 33 tons repectively - I'm not sure you could create a solid tire that would be of much absorbtion value under those conditions. There is, of course, the weight to consider (even filled with nitrogen, they're heavier than you might imagine) but aside from that, when the tires are inflated correctly they're better able to flex and keep heat build up to a minimum.
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It's cute, but...where are the fifth and sixth engines?