BattlePope

I completely agree that "lack of previous students" has a negative connotation. With that said, I would still like to try to incorporate that sentiment into my statement somehow. I feel that it lets the admissions committee know that I am familiar with Dr. Johnson and have a specific reason for picking him. I also feel that a statement along the lines of what you laid out is fairly generic and doesn't have that same specific "I know this professor well and know why he would be good for ME" feel to it. I do like the use of "accessibility" though. Maybe instead of "lack of previous students", I could say something like "fledgling lab"? I feel that that statement has less of a negative connotation. 
 
Or maybe you're right and I should just go with something similar to what you mentioned. Thoughts?
 
Edit: Thanks for the help by the way! I really appreciate it.