The wheels don’t do any acceleration so that is not an issue. They just need to roll and break after landing. The wheels themselves are very heavy duty and usually come in pairs (or even more). They are changed quite often because they lose some rubber every time the plane lands. You can see the black skid marks they leave behind on runways. The brakes aren’t fundamentally that different but they too have to be quite heavy duty and fault tolerant.
Now for the real question of why it makes sense for the wheels to be small. Larger wheels would have a higher moment of inertia. That would make them drag a lot more when landing until they get match the speed of the aircraft. Smaller wheels have a smaller moment of inertia so they match the speed sooner. Some planes have relatively large wheels. They are needed to be able to land in the wilderness or outside paved runways at least. They also come in rather slow, so it doesn’t take much for the wheels to match speed when landing.
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