How much denser do batteries have to get to feasibly power a large commercial jet from SF to LA? Do they need to include two of these inverters for redundancy?
Electric flight does not have this problem and nor does it have the scale advantage. Flying smaller electrical planes is more efficient on a kwh per passenger basis. It's also easier to build them technically.
The SF to LA route is well in range for the Eviation Alice that should hit the market in the next few years. The variant they are advertising carries 9 passengers + 2 crew or 1,250kg of useful load for a bit over 1000 kilometers (including the required extra range) using 900kwh of batteries. This thing is supposedly entering certification after next year and should start hitting the market in a few years.
This is obviously not a jet but the economics of flying this thing are very different. It completely destroys the business case for that. You charge it with cheap electricity. The unit cost is in the order of 3M$, it can fly in and out of any small airport, and it makes a lot less noise. One full charge would cost about 50-100 $ depending on how cheap you can get your electricity. Probably lower than that given improvements in cost of e.g. solar.
For the price of 1 737, you could buy a few dozen of these. It can do a lot of things a big noisy jet can't do while being cheaper at it. Imagine a fleet of about 10000 of these flying back and forth all over California to any of the dozens of small airports. Deploying that amount of planes will take a few decades probably. Over that time you can expect improvements in range, battery efficiency and economies of scale. So, bigger, faster, cheaper happens as well.
I'm not sure it will ever make sense to cram hundreds of people in an electrical plane. But why would you want to when the small ones eventually drop in price to a couple of tens to hundreds of K each and fly you from A to B autonomously for the price of a cup of coffee?
Probably a smaller plane takes less time to taxi, take off, land, etc. Still it seems like if you increase significantly the number of flights in and out of an airport, you'll run into some serious congestion issues.
Additionally, you could build dozens to hundreds of airstrips in and around big cities. The Eviation Alice still takes off horizontally. But there are plenty of vtol designs out there as well.
The real issue is going to be upgrading ATC to deal with thousands of vehicles flying at the same time. Current operations with it's roots in analog technology from mid last century is just not going to scale for that.
Currently the cost of pilot and co pilot are amortized over 100s of passengers.
You've quoted 2 crew to 9 passengers, and I'd have guessed 3 crew (pilot, co pilot, Air Host(ess))
Obviously when we get to autonomous flight that will change, flights will never be completely crewless though.
You might want to ditch those empty batteries also at the right point :)