Welcome to e-budo!
I've personally never heard of the term "sport jujutsu" myself, so I looked it up. Looks like some organization (the JJIF?) has created competition rules for their own form of jujutsu. Therefore, it seems to me that your basic premise is in error. There is indeed a term called "sport jujutsu".
Jujutsu, 柔術, as we know, is simply a descriptive phrase referring to Japanese unarmed arts. There is not now, nor has there ever been, a strict definition of what constitutes jujutsu. For that matter, the Japanese language precludes strict definitions for just about anything.
Now you could make arguments over the fact that "sport jujutsu" has no basis in traditional Japanese arts, or that "sport jujutsu" is ineffective or useless for the original use of jujutsu. You can argue that it
shouldn't exist, but you can't argue that it doesn't exist, since those actually doing it would disagree.
So, do you have an alternate point, since your original point seems to be in error.