Why doesn't a capacitor connected to a MOSFET charge to VDD
The voltage that must be greater than \$V_{TN}\$ is the voltage from the gate to the source, \$V_{GS}\$, not just the voltage at the gate. Once the source voltage rises to \$V_{DD} -V_{TN}\$ the voltage from the gate to the source will just equal \$V_{TN}\$. Any increase in the source voltage will cause \$V_{GS}\$ to be less than \$V_{TN}\$ so current flow will stop. Therefore, the voltage at the transistor's source can't rise above \$V_{DD}-V_{TN}\$ (based on this simple model).