Airliners have already moved away from the hub-and-spoke model to a point-to-point model where smaller narrowbodies fly direct from small airport to small airport (E.g. Southwest in the US). They do this specifically because of the increased efficiencies of smaller aircraft.
If you can further lower the per passanger cost of small planes, you can make smaller airports more viable, and fly point-to-point from more odd routes. Think Oxford, UK (OXF), to Gothenburg, Sweden (GSE).
The third expensive component is staffing. Pilots are expensive and for complex aircraft they need lots of training. So, simple electrical airplanes lower the training cost and make it easier to train and find new pilots. And complexity is also a reason you often need two pilots. Smaller/simpler airplanes can be one pilot operations. And of course replacing pilots entirely when these things become autonomous brings further cost savings. The flip side is that lots of small planes require more pilots.
Finally, big airports are expensive. You have to pay landing fees in lots of places. And service fees. And missing your assigned slot because of delays is expensive. That too goes away if you start flying from less busy/cheaper airports.
So, there a few additional savings here beyond fuel. But that is the biggest one.
IMHO this is going to be a repeat of the EV revolution a decade ago. But minus a lot of the emotional bickering about range anxiety, etc. Most planes are operated by for profit businesses. The second something cheap becomes available, they'll be all over it. In the same way using electrical vans vs. ice vans is not a topic of debate in the industry. You get the electrical van if you can. They are cheaper to operate. There's zero uncertainty on that front so you see essentially all large fleets transitioning to electrical vans as soon as they can get it done.
With electrical flight, a lot of this stuff is bottle necked on product development (happening), certification (starting to happen), and volume production (not happening yet). Better batteries increase the demand further. But without volume production, demand is not the issue. Supply is. This is and will be supply constrained for a long time.
This is simply not true with electrical planes. A mega watt hour of power is about 60-100$. And much cheaper than that with renewables. Not at retail prices of course. But if you consume power by the mwh, you'd be investing in your own generation (solar + storage) pretty soon. A mwh is about what you need to move a small electrical plane a few hundred miles. The kerosene cost for a similar journey in a small jet is going to be hundreds of dollars, even for a small jet. The smallest jets burn 50-100 gallons of fuel per hour (in cruise). Depending where you get your fuel, that ranges from 3-5$ per gallon. That's why small jets are only for rich people. Even a very short flight sets you back hundreds of dollars. A simple propeller plane is cheaper. But we're still talking 5-10 gallons per hour. That's why people talk about 100$ hamburgers. Because that's what it costs to take your tiny plane out to grab a burger somewhere.
Big big jets are a bit more economical with fuel than small ones. But they only makes sense if you can distribute fuel cost among many passengers.
With electrical, you can use lots of smaller planes cost effectively rather than having to put lots of people in a few bigger ones. For the same reason, you don't need big airports either. Or worry about pollution. And even the noise of small electrical planes is not as much of a problem. And with autonomous flight, we won't even need pilots long term. Small electrical planes are good enough and much nicer for passengers, more flexible to operate, etc.