although AC units seem to be fine for the drivers, sitting in the pits or the paddock...
The driver is important. They've got to do 10-20 corners a lap, for 50-70 laps without making a major misjudgement in changing conditions and while dodging (or better passing) the other drivers on the track. Sometimes at 200mph and at some considerable risk to their lives. In an ideal world they won't even make many minor misjudgements - because that means they go faster and put less stress on their tyres.
Compare in-car footage of Lewis Hamilton to most of the other drivers, and notice how many fewer inputs he makes on the steering wheel mid-corner. This is because he is one of the top 3 F1 drivers of all time and is extraordinarly good at this. He's turning the wheel once at the beginning of many corners knowing where the car will be at the end of the corner, so he doesn't have to adjust the steering later to correct it. And he's consistently better than most other drivers at doing this. This means his tyres wear out less quickly, so he can either use that saved rubber to go faster, or to go longer without changing them. To concentrate like that for 2 hours, in a hot uncomfortable car while being distracted by all the stuff that goes on around him means that he needs to be delivered to the car fresh at the start of the race. Calm, cool and collected. And it's easier for your driver to do that mental preparation if he's relaxed and not hot and sweaty. Or in the case of James Hunt - if he's just had a few bottles of champagne and page 3 girls in his bed all night... In an ideal world you'd control everything and have it all perfect - but where that's difficult or impossible you have to prioritise. Which means drivers and cars first.
Also some of that air-con is provided in the racetrack's buildings - which you don't have to ship everywhere with you. Plus every power requirement that you add, is more power you've got to get trackside (and might not be able to) - or run generators for.