Well, they would be reporting to him on security matters, not on crew performance.
At least, there's one security guard stationed in every department on the ship, and the department heads tell him if his security are doing their jobs and the security tells Tuvok if the Department heads are doing their job.
The Doctor (in Flesh and Blood & Equinox.)
Janeway (Well, the Doctor, but that's thepoint.) in Renaisance Man.
Or less insidious incursions like Quicksilver Tom and Harry.
Tuvok should have been fired for letting 40 aliens traipse about Voyager unchecked for months in Scientific Method.
Both times it happened (Flesh and Blood again.).
Seriously, Seska had a murderous hologram programmed to kill every one if she'd disappeared for two years, but Tuvok just lets Aliens take his ship without the merest hint of a booby trap.
Is Neelix a department head, or is the hedhog under the umbrella of whoever is in charge of the replicators?
I'd guess that the number of the 13 departments are in escapable no matter the size of the ship, even if the man power and admin looking after all those departments is consolidated.