Working of NMOS as a capacitor
If drain/source is connected to VDD, its as good as open (0 capacitance)

That is not true, you get less capacitance but not zero.

How to reason out the need for large length and small width?

Also a wrong assumption, any size of MOSFET will work as a capacitor. The series resistance of the capacitor is generally smaller (you get a "better" capacitor) when the width is large and length is small. But in practice I usually make these MOS capacitors (somewhat) square as that is a good compromise between series resistance and capacitance per area.