If it was possible to make an aircraft with no wheels, then they would. Wheels are a necessary evil. They only add weight and contribute nothing to the aircraft performance once off the ground. The undercarriage is used for the first 1% and the last 1% of the journey, and the fuel cost in carrying a heavier weight which is stowed for 98% of the journey is crazy.
When aircraft are using tires at any speed it's mostly for going straight, taking off or landing, so they don't need the wider tires that cars often need that are good for cornering. Airplanes rarely have to brake hard because pilots plan their landings such that they slow down both using aerodynamic drag and the runway lengths allow them to slow down without as much braking. Runways are flat and smooth, which means aircraft can get away with smaller tires compared to vehicles that must handle rough terrain.
On higher performance aircraft, when the landing gear retracts it's difficult to do with large wheels and tires. The wheels must fit into wheel wells when retracted after takeoff, and wheel wells take up space for cargo and fuel. Small wheels are lighter and fit in a smaller space, both good on an aircraft where space and weight are limited and carrying passengers for a profit is the goal. As the technology of brakes and rubber and metallurgy have advanced, so wheels have gotten smaller.
There is a type of aircraft designed to operate off of unimproved terrain that often uses very big tires. They use larger low pressure tires to handle the bumps and rocks that normal aircraft don't have to deal with. The early B-36 Peacemakers had a single huge mainwheel under each wing, and the Americans only had three airbases with surfaces strong enough to withstand the pressure that wheel was putting down. Production B-36s switched to multiple-wheel bogies and could land at many more airbases. Designers will shave off every last useless ounce that they can in the search for more efficiency, and for most aircraft operating on paved runways, smaller wheels do the job perfectly well.