I don't know for sure, I can only bring additional intel, and a theory.
This convention already existed in ANS X9.62-1998, section 4.3.6 Point-to-Octet-String Conversion, which also assigns $06$ and $07$ to indicate another 'hybrid' encoding method. Just like in compressed form, the parity of the format indicator encodes a quantity. Quoting:
The octet string representation of the point at infinity $\mathcal O$ shall be a single zero octet $PC = 00$. (…)
If the compressed form is used (…) Assign the value $02$ to the single octet $PC$ if $\tilde y_p$ is 0, or the value $03$ if $\tilde y_p$ is 1. (…)
If the uncompressed form is used (…) Assign the value $04$ to the single octet $PC$. (…)
If the hybrid form is used (…) Assign the value $06$ to the single octet¹ if $\tilde y_p$ is 0, or the value $07$ if $\tilde y_p$ is 1. (…)
So my theory is that bit 0 of the identifier $PC$ is reserved for an additional bit in formats where that makes sense, with the format itself encoded in the other bits of PC. Thus $01$ and $05$ are unassigned, because there is no additional bit to be coded for the point at infinity or when using uncompressed form.
Notice that the point at infinity is not a valid public key in ECDSA, and would be a lousy one.
¹ sic: the mention $PC$ is missing.
