It is important to think about these things. However, not having a mentor has not been an issue for me or any of my peers. We have a research advisor (mine has been amazing) and an internship advisor. I have worked closely with my dissertation committee and have been very pleased with the amount of support that I have received. You are making an assumption based on size, without looking into the actual program. I understand that the program may not be for you (and I am not advocating that anyone come here, just giving another view on my experience) but assumptions without further information is unfair.
It's great that you receive sufficient attention from your research advisor and your internship advisor. It would be even better if this is the norm for larger programs. The truth is, even in smaller programs, big name mentors might not spend any time at all with 1 or 2 mentees. However, why set oneself up for the greater likelihood of not receiving this necessary attention by entering a large program? It's math.
Also, I agree that the person factor is huge in any selection process (internship/job). But before employers can use their Axis II/no people skills checklist on their candidates, one still needs to make it to that stage in the first place. And it seems that carrying a the professional school name tag tends to hinder one from reaching that stage to show your true skills and talents.