MOSFET chip for discrete CMOS inverter

You can now get individual SMD inverters like this one, which is just one of the six gates found in a classic 74AHCT04 style package.

Logic gates get faster when the supply voltage increases. What you call the "time constant" of the charging path, isn't constant: it depends on supply voltage. If you think of it as an \$RC\$ circuit, the capacitance \$C\$ remains roughly constant, but \$R\$ decreases with supply voltage (remember that with increased \$V_{GS}\$ on a transistor, its resistance goes down), so \$RC\$ goes down.

A more accurate way to think of it is this: the voltage swing increases with supply voltage, so to maintain the same speed the charging current should also increase with supply voltage (remembering the capacitor equation, \$t=\frac{CV}{I}\$). However, for MOSFETs in saturation, the charging current increases roughly with the square of supply voltage (remembering the MOSFET equation, \$I_D=k(V_{GS}-V_{TH})^2\$). Thus, the time spent charging goes down.

This is true up to a point: once the transistors get small enough so that they no longer follow square-law behavior (because of velocity saturation), the logic gate speed no longer improves with increased supply voltage (because the charging current no longer scales with the square of \$V_{GS}\$, but instead scales linearly). Thus, for the latest process nodes, don't expect to improve speed by changing the supply voltage.