We want to increase gate capacitance, not decrease it. The higher the capacitance, the faster you can invert the channel, and therefore turn the transistor on.
Think of a transistor as a water tap (valve based). Gate capacitance is the sensitivity of the valve to the handle. In this analogy, higher capacitance is equivalent to less effort to turn the handle (to move the valve out of the way and let the water flow).
That's the reason we want to increase the area of the gate (the idea behind FinFET, and all-around gate), and increase its dielectric constant (the idea behind high-k materials).
You're also confused about RC model - perhaps you heard it in the context of a logic gate (as in NAND), and you try to apply it when talking about a transistor gate (as in FinFET). Nope.
So transistors in modern processors don't end up switching consistently. There is all sorts of error correction to compensate for that, but it only goes so far.
http://spectrum.ieee.org/semiconductors/design/the-highk-sol...
This is exactly correct. Even at 28nm, many SoCs are intentionally using less than the max manufacturable transistor density, due to dynamic power/thermal constraints.
SRAM is scaling poorly too. It makes up 50-60% of many SoC designs yet at 1500MHz+ its density (Mb/mm^2) looks likely to increase just 1.1X between 28nm and 16nm.
Desktop CPUs are not going to get 32MB on-die caches any time soon. At least not without eDRAM.