  Terrestrial planets are easier to detect around M dwarfs than other types of
stars, making them promising for next-generation atmospheric characterization
studies. The $TESS$ mission has greatly increased the number of known M dwarf
planets that we can use to perform population studies, allowing us to explore
how the rocky planet occurrence rate varies with host radius, following in the
footsteps of past work with $Kepler$ data. In this paper, we use simulations to
assess $TESS$'s yield of small ($0.5\,R_\oplus \,<\,R_p\,<\,2\,R_\oplus$)
planet candidates around nearby ($d\,<\,30$ pc) M dwarfs. We highlight the
underappreciated fact that while $TESS$ was indeed expected to find a large
number of planets around M dwarfs overall, it was not expected to have a high
planetary yield for the latest M dwarfs. Furthermore, we find that $TESS$ has
detected fewer planets around stars with $R_*\,<\,0.3 R_\odot$ than even was
expected (11 observed vs. $24\,\pm\,5$ expected). We find evidence that the
photometric noise of stars in the $TESS$ bandpass increases with decreasing
radius for M dwarfs. However, this trend cannot explain the observed
distribution of planets. Our main conclusions are: (1) the planet occurrence
rate likely doesn't increase, and may decrease for the latest M dwarfs; and (2)
there are at least 17, and potentially three times that number, transiting
planets around nearby late M dwarfs that still won't be detected by the end of
$TESS$'s 4th year.
