If your body needs to devote resources to both doing new work and rebuilding from previous work, your rest is going to be less effective. Full rest days are better than partial rest (ie. resting legs while working on upper body). Your strength gains will suffer if you are doing cardio on days that could otherwise be rest days. It would be better to do cardio on the same day as you lift, leaving a full day off from any activity.
Also, it's very tricky to properly schedule a split routine like you're trying to do. From Mark Rippetoe's Practical Programming:
A common way to organize training among recreational lifters and
bodybuilders is a "split" routine, where one body part or "muscle
group" is worked each day, until the entire body has accumulated a
workout. If "chest" is only trained once a week, even though training
may occur several days per week, "chest" will not receive enough work
to constitute overload, and optimal adaptation cannot occur. By the
same token, "chest" will usually include triceps, since the bench
press is the favorite chest exercise; if "shoulders" involves
pressing, "arms" get their own day too, and "back" really means lats
and therefore lat pulldowns or chins, it is possible to expose the
triceps to four or more workouts in a week. This is an example of poor
training organization producing a schedule that includes both
inadequate and excessive exercise frequency.
Further, unless you are an advanced trainee, there's no need for complicated scheduling.