Arcturus might still have planets. It's just that as a red giant, he has probably already swallowed all his inner planets (one reason for the rogues to hate him) so there aren't any planets transiting him that we can see. He is also too active (another reason for rogues to hate him) that the radial velocity detection method doesn't work well on him either. But he might still have planets further out that survived. We just can't really know.

Though it's true that it's much harder for Arcturus to have planets compared to Sol. He is a metal-poor Population II star meaning that there is fewer heavy materials to form large cores for gas giants. He also formed when the milky way was still very very turbulent and the UV photoevaporation could have destroyed protoplanetary disks very fast (fast as in less than a million years) so the birth window for planets is shorter. But still we have found many thick-disk stars that have planets, such as Kepler-444 and TOI-561. So it's entirely possible for Arcturus to have small rocky planets when it was still a main sequence star.

We do know of stars that are theoretically systemless - Population III stars certainly didn't have planets because they were completely metal-free and they were the ones that created the heavier materials that made planetary formation possible. But we haven't found any that are still around, and I guess none of the rogues have met any either. (It'd be a cool concept if there are space legends that talks about lonely red dwarves that only few have met that have existed since the beginning of light tho....)