Especially given the current trend in automation, the risk that a relatively small group of capitalists will slowly take full control of almost all the means of production is real.
Another huge problem of having a world run by corporations is the environmental situation. Personally I cannot accept a world where profit is considered more important than the environment to such an extent.
I don't know what the solution to this problem may be. Alternatives to capitalism have been proposed in the past, and are continuously studied now, but shifting to another economical system would not be easy, if possible at all at this point.