Also, I like to play basketball a couple times a week. You would be very hard pressed to suggest that doing that is hurting my martial arts at all, especially since I do it on my lunch break so it doesn't get in the way.
If I went to a judo club, and did it casually during the time I now play basketball, just to get more used to grapplers, how would that hurt my understanding of kempo? I would definitely not be "very good" at grappling (It would take me forever at that schedule to even become somewhat proficient), but I don't see how it would impact my kempo since it would not be taking time away from training kempo, and it's at a time I'm generally not thinking about kempo in general.
The only way your claim that you can only be very good if you only practice one art makes sense to me is if you also believe having any hobbies outside of martial arts will prevent you from becoming very good at them.
You are correct in that one can very well do a variety of physical and mental activities very well. Nobody would argue against that.
However there are pitfalls in doing so with several martial arts, and I will attempt to describe what I mean and when these pitfalls rear their heads, as they are not absolute and are not necessarily a problem in every case. This is why my own advice to the OP was intended to make him aware of these possibilities in advance, and not as an attempt to dictate to him what he is allowed to do.
Different systems use certain biomechanics as well as physical practices designed to use those biomechanics, in developing their techniques. This is a process, it takes time and repetition and effort, and consistency.
Different systems can use the biomechanics differently, and they can bring different methodologies into play, when developing their techniques. They can also use similar biomechanics, but use different methodologies and physical practices to develop their techniques including for the same technique used by other systems.
Take the seemingly simple punch, for example. If you look at how the punch is trained by a boxer, a shotokan guy, a wing chun guy, and a white crane guy, you will see that their methods go about it in different ways. If someone wanted to train all of these systems simultaneously, well fine. But there are problems.
While training a punch, a technique shared by all of these systems, you would be doing so in four different ways. That is a waste of time and energy. Each of the four methods would develop your punch half as well in four times the time and effort. If you focus on one method and develop your punch in a consistent manner, your punch will be twice as good in a quarter the time. You have no need to develop the same technique using four different methodologies. In the end, you need a good punch. One consistent method of developing that punch will serve you best.
In my own experience of training multiple systems at the same time, I could tell that the time I spent practicing punches according to the methods of one system, was disruptive to my development in the other system, and vice-verse.
So that is the kind of issue that can arise. Gaining ground in one system can cause you to lose ground in another. Yes, this absolutely can happen.
Some techniques are designed to work with a specific kind of foundation. If you try to work those techniques from an incompatible foundation, they don't work well, sometimes they don't work at all. This can happen if you are trying to mix systems that are fundamentally incompatible.
There are other cases where these conflicts do not happen. But being aware of these issues is important for someone who might consider training in a second or third or fourth system.
Some things do not mix well. Everyone wants to add to what they do. People forget to consider that maybe some things should not be added. Some things you are better off without.