The limiting factor in F1 these days is the driver, there was a great article in Popular Science about it. Without worrying about keeping a driver alive (and conscious), the cars would be substantially faster. They also talked about how physically demanding driving an F1 car is, and how a driver is basically an athlete in prime condition. In keeping their heads upright through turns they develop some ridiculous muscle in their necks. There's a funny video on youtube of an F1 driver crushing a walnut with his neck.

If it was legal, there would be two or three engineers remotely controlling all those knobs and buttons. F1 rules ban any aspect of the car from being controlled remotely or automatically and mandate a spec ECU.

It's unlikely that they would drive by remote control as feel is so important - a racing driver relies on his backside as much as his eyes. Drivers use physical sensation to feel the limit of grip and the balance of the car, something that would be very different to control remotely.

You could potentially go much faster without drivers, as cornering speeds are artificially limited by the rules to maintain driver safety. The severest corners in F1 induce 5G of lateral force. Inexperienced drivers often spend later laps of a race resting their head against the side of the cockpit, as their neck muscles are exhausted.

In a completely free racing formula, cars would have vast amounts of mechanical grip and downforce, weigh next to nothing and corner so fast that no human could survive a lap.

I don't see how this makes sense. As demonstrated the drivers have a lot of controls that are traditionally pre-set BY the engineers. The engineer is moving into the car, if anything.

I don't think you can make the driver obsolete. Perhaps some day they won't be physically sitting in the car, but I don't think logics alone can win a race. You need someone in control with a good mix of instincts, timing, and brashness to win a race.

Could probably do it now, but no one would watch.