Why aren't there many (voltage controlled) variable capacitors above ~1000pF?
Voltage controlled capacitors (varicaps or varactors) are diodes.  

A reverse biased diode acts like a (small) capacitor.  The capacitance varies depending on the applied reverse bias voltage.

Varicaps are designed to have a larger capacitance than normal diodes.  Still, you are limited in the amount of capacitance you can squeeze into the junction of a single diode.

Driving a varicap usually requires a little bit of surrounding circuitry to keep the DC from getting into the tuned circuit and to keep the RF from getting out over the DC supply:



Image from Wikipedia

All of the ones you linked to are four port devices that include most of the supporting circuitry.

In many RF circuits, it is common to use an inductor to couple in the DC control voltage rather than a resistor.



Speculating, I'd say its just too difficult to make diode junctions with really high capacitance.  I'd also bet that the maximum capacitance has an effect on how fast you can vary the capacitance - I expect a bigger varicap will change capacitance in response to a voltage change slower than a smaller varicap.