.22 LR uses an outside lubricated bullet. The bullet diameter is the same as the case diameter. There is a heel of the bullet that is considerably under bore size that sits inside the case. Most .22LR bullets are soft swaged lead that is relatively easy to make. Sometimes these bullets are copper washed, mostly they are coated with a lubricant. To make a jacketed bullet that will fit inside the case, expand at the base upon firing to make a good gas seal and bite the rifling at these relatively low pressures and velocities would be a daunting task. Could it be done? Probably. It would be prohibitively expensive and would ruin the inexpensive appeal of the rimfire ammo.
In short, it would cost more than people are willing to pay for .22LR ammo.
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"Robo is right" Fuzzball