We present a generalized gradient approximation kinetic energy functional family with a simple rational form and nonempirical parameter derived from the semiclassical energy expansion of neutral atoms. The family unifies the Pauli-enhancement-factor-based semilocal noninteracting kinetic energy functionals (known as Pauli functionals) that achieve good, balanced accuracy with respect to metallic and semiconductor systems. We show that these functionals' performance can be understood in terms of the small-$s$ expansion, where $s$ is the reduced density gradient. We derive Pauli functionals parameters from the large-$Z$ kinetic energy limits of neutral atoms, which prevents overfitting to bulk systems. These results spotlight the current state of the art for semilocal kinetic energy functionals. For the next generation of functionals, including more constraints and variables, these results would allow to fix second-order coefficients nonempirically and concentrate on exploring next-order terms in the small-$s$ expansion.