In Jonathan Katz and Yehuda Lindell's Introduction to Modern Cryptography (3rd edition), the key generator of e.g. signature has
The key-generation algorithm $\mathsf{Gen}$ takes as input a security parameter $1^n$ and outputs a pair of keys $(\mathrm{pk},\mathrm{sk})$. These are called the public key and the private key, respectively. We assume that $\mathrm{pk}$ and $\mathrm{sk}$ each has length at least $n$, and that $n$ can be determined from $\mathrm{pk}$ or $\mathrm{sk}$.
I see why the minimum size of $\mathrm{pk}$ and $\mathrm{sk}$ must grow with $n$ (with some minimum rate) in order to meet any sound security definition, but not why that's made a requirement.