Thanks Oldsalt, some interesting comments. Generally with karts, the inner race is secured in position on the axle with locking collars. I normally install locking collars on both sides of each bearing. If you don't anchor the inner race against horizontal movement on the axle, you will have trouble with chain alignment and the rear brake rotor dragging because the axle will shift relative to the chassis when cornering.
The outer race is generally mounted to the kart bearing hanger with cassettes that allow the bearing to float as the axle and chassis flexes. Generally, kart axle bearings will last a long time, unless you race in the rain, or clean them too much and introduce contamination.
Years ago, 1 inch rear axles were common, my kart is 1986 vintage. Today, although 1 inch id axle bearings are available, I don't know where to get free spinning that size. Today, 1.25 inch, 40mm, and 50mm axles are common and
free spinning axle bearings lubricated with light oil are generally available for not a lot more than standard bearings lubricated with grease.
I think the mini drag bike racers are using 1 inch for the nice sprocket and brake hubs that are readily available for 1 inch axles and not available for smaller such as 3/4 and 5/8 inch generally used with minibikes.
Thanks