Your question body is different from your question title and it seems you really want to ask what you did in the question body so I'll address that.
Short Answer: The simple power law which applies for larger asteroids and comets actually doesn't extend that well to smaller bodies and shouldn't be trusted too much in that range.
You're right to be suspicious of using a simple power law to relate asteroid size to quantity at small sizes. Especially because there are known deviations from that power law at certain radii. As wikipedia notes:
The number of asteroids decreases markedly with size. Although this generally follows a power law, there are 'bumps' at 5 km and 100 km, where more asteroids than expected from a logarithmic distribution are found.
Who's to say there aren't other bumps or deviations at radii that we can't observationally confirm. Our confidence in any power law's applicability for small asteroids and comets basically comes from modelling.
This power law you're asking about is essentially something referred to as an "Initial Mass Function" (IMF). A lot of work has been done to define an IMF for stars, relating the mass of stars to the number of stars at that mass. This stellar IMF follows a power law more or less, but strongly deviates for very low masses. At the surface, it would be reasonable to assume an IMF for asteroids and comets likewise deviates.
The way you answer this, is through models. See for example Cuzzi, Hogan, and Bottke (2010) (that link is to the formal journal paper, but for some reason some plots are obscured so you can also look at their "unofficial" arxiv version). In this paper, the authors attempt to construct a representative asteroid/comet population by modeling their formation via accretion of protoplanetary dust grains into asteroids, comets, KBO, and planetesimals. They make certain assumptions about the initial gas disk around the Sun and bake in physics of how these dust grains formed into larger conglomerates. Their end goal is to produce an IMF that identifies how many asteroids/comets exist at a given size. They back up a lot of their modelling with data from observations so they stick to reality as much as possible.
I'll let you peruse their results since they actually produce many different IMFs using a variety of different assumptions and starting conditions. However, I think one can summarize their results in a way which addresses your main question. As they state it:
Asteroids were born big
What they mean is that asteroids (and comets), rather than forming by successive growth via accretion of many small particles, seem to just clump together into larger bodies, completely bypassing the formation of many smaller meter-sized asteroids and comets (that's not to say there aren't meter-sized objects). You can actually see this in their various plots (fig. 4 for example). Much like the stellar IMF, the power law drastically changes once you get to small sizes and the power law which applied for larger sizes is no longer applicable. At which size the general power law no longer becomes applicable depends upon certain tunable parameters. Cuzzi et al. shows many different results with their tunable parameters set to many different possible values.