Let's work out some numbers.
Picking a DJI Phantom 4 as a 'typical photo drone' example, it's battery is 4s 5350mAh and weighs about 500g, and provides about 20 minutes of flight time.
That implies that the motors are using (5350/1000)x(60/20)=15amps (converting mAh to Ah, and minutes to hours). At 15v that is 225W for flight.
The question talks about using 'static electricity high voltages' - but the most noticeable feature of static electricity is that it can spark across gaps. 10,000v will jump 3mm or so in dry air, and 3000v will jump 0.5mm. However I don't think we need to go that high. Stepping the voltage up 100 times to 1500v would reduce our current to 0.15a.
That means we could use 29AWG wire, which is 0.3mm diameter - at that point the insulation may be heavier than the wire. According to that chart, 29AWG has a breaking strain of 3.6lbs, which is much more than the weight we have saved from the battery so we don't need to worry about the wire breaking under its own weight.
So how long could the tether be? 29AWG weighs 0.3863 lbs per 1000ft (or 175g for 300m). We will need two strands (350g), so 1000ft (300m) of cable uses up most the weight we've saved by eliminating the battery, before adding any insulation or the transformer. 1500ft of wire would be heavier than the battery.
* yes, you could hover at normal photography drone heights for an unlimited time using a tether.
* The weight of the wire prevents you going much higher than 1500ft.
* The weight of the insulation prevents you using lighter wire.