The problem is a simple one. Although great care is typically taken by spindle manufacturers to produce units that run fast and true, the spindles are used to carry tools. A solution, of course, is simply to balance the tools before they are placed in the spindle. This is a good practice regardless of the spindle speeds, be it high or low. But there can be some balancing problems remaining when the tools are to be run at high speeds because chances are the balancing has been performed at low speed.
Dynamic behavior is different at high speeds as compared with low.
Engineers there concentrated on balancing grinding wheels. Apparently, the systems they supplied worked well, based on studies they collected from installations on grinders in sites including the Ford Cleveland Engine Plant 1, the Chrysler Trenton Engine Plant, Cummins Jamestown Engine Plant, and others. But there isn't a direct translation from grinding machines to machining centers, even higher speed grinders. At issue is the fact that grinding wheels tend to be setup and run for a long time, at least compared to the tools in a machining center. Machining center tool changes are typically frequent.