However they are a lot more expensive to run and maintain - eg. just think about the additional moving parts and friction.
Also it's possible they do different damage - the metal treads are not as forgiving as soft balloon tyres.
Key technology of electrification would be tethered drone swarms that feed from the cable they carry, because I'd assume that you'd want to separate batteries from your actors so that they are flexible you work from grid infrastructure just as well as from some battery truck tagging along on an access road (which brings us back to surface load, you wouldn't want the battery loading soil you still want to grow in).
I will say (because this is obvious from public information) that we are "looking" at electric tractors, but making them work is hard. 10 years ago we stuffed as many batteries as we could in a 100 horsepower tractor, and for 45 minutes it when head to head with a similar diesel tractor, then the batteries were dead. 100 horsepower just above a small tractor these days. Remember a Tesla might be able to produce 500 horsepower (I can't be bothered to look it up, but something very large like that seems reasonable), but to maintain speed on a freeway it only needs about 20 horsepower. A tractor is expected to produce the rated horsepower for 10 hours non stop.
Your idea of a feed cable is something we have looked at (you can find an announcement, though it might be in German). There are a lot of issues with making it work in the real world, though it might be where things go if diesel gets a lot more expensive.
Basically when ya chart out gravimetric and volumetric density stuffing batteries doesnt seem to make sense. There may be some other options (feed cable, slower cycle, etc.)
It seems people (outside the agriculture industry) underestimate what todays tractors (and even more so harvesters, etc) can do and how much power that requires. Harvesters running 12-24 hours a day for days or weeks seem way out of reach of what the current battery technology can accomplish.
I'd bet on hydrogen engines (at least in the next 5-10 years) for larger machines.
On the other hand tractors are multipurpose tools and it highly depends on what it will be used for. If the tractor is only expected to run a few hours a day then batteries might actually work
Since the infrastructure already exists wherever there is serious agriculture, we should probably call that "liquid anhydrous ammonia engines". NH4 is a more practical carrier for hydrogen than its elemental form.
But part of the appeal of a big powerful tractor is their huge versatility - you'd loose a lot of that if you needed additional infrastructure in place.
Obviously the pressurised air itself has mass, but I think its more to do with tyre deformation modifying the contact surface area. The air inside is just to distribute the load across the contact area.
Tractors on tracks, yes.
My speculation: you only harvest in dry weather (so traction differences don't matter), and harvesting goes faster than say tilling, so maybe tires are preferred. You'll also see big fleets of combines going down the road to the next field; I think tracked vehicles are frowned upon on public roads.