I think flying could be made cheaper and massively more convenient by getting rid of airport security the way it is done right now. Imagine planes being boarded like trains: there might be a security tradeoff but it would be offset by the massive time benefit for everyone involved. I know I would take that risk, I consider my own time to be more worthy than TSA considers it to be
As an example: planes almost never crash. Which is great! So you could drop the requirement to carry life-vests, without compromising safety numbers.
(If you want, you can invest 50% of the cost savings into eg anti-malaria nets, and you'd come out way ahead in terms of lives saved.)
Similarly, airplane seats are massively over-engineered. You could loosen restrictions there, and save weight and thus costs.
I think Japan might already have different domestic regulations there. I remember being on a domestic flight between Kobe and Tokyo, and the seats in economy class used a lot of mesh over aluminium frame or so. They looked a lot lighter (and also more breathable) than your typical airplane seats. See https://photos.app.goo.gl/ZDWQTNMB93mQs5Yz5 for a picture that I took.
I also agree with vlack-vingaard, but they already gave some good examples.
We already know cheap flying with current safety standards is economically viable, with costs approaching the cost of fuel; see low cost airlines like Ryanair. So the most effective way to lower prices is for airlines to downgrade amenities and services onboard.