First, I applaud you on your conclusion, because I feel that point is lost on many who seem to view the present state as some ordained condition to extend through all time.
Air travel has been transformational, fast, reasonably convenient, and cheap. It's also been an accident of geohistory, in many regards. The coming / current fuels transition will raise the costs of many things, transport included, and air transport most especially. One of the lessons of history is that the consequences of costs falling, as many have through the industrial revolutions, have subtle and profound influences, mostly unanticipated by those who first started down specific technical pathways.
My sense is that rising costs will operate similarly. We'll have much of the knowledge and technical understanding achieved over the past 200 years, but we'll see costs rising or capabilities falling in many domains. And that will have profound and subtle ripple effects.
Small aircraft may be possible, and perhaps slow airships, but the era of mass bulk human transcontinental transport, quite probably not so much. Or possible, but at prices at some multiple of today: 2x, 10x, 100x, 1,000x. Or transoceanic travel of 1-3 days, rather than 6-18 hours.
Getting back to airships: there are only so many materials available. An airship requires some sort of frame, some sort of lifting gas containment, motors, an energy source, and passenger or cargo facilities. Even excluding hydrogen as a lifting gas, they've proved expensive and dangerous. Vehicles such as LEMV / Airlander 10 are not strictly rigid, but is in part supported by pneumatic pressure. The craft itself was written off after coming loose from moorings in high winds.
Top speeds will be on the order of 160 - 240 kph, rather than 1,000 kph for jet aircraft. Flight levels will likely be < 1,000 meter -- Hindenberg cruised at 300m, though often much lower. That's well into weather, which airships handle poorly. LEMV had a requirement to operate to 20,000 ft (6,000 meters), though it only reached 3,500 ft (1,000m) in testing.
I've watched and read breathless accounts of an airship revival for decades. To date they've failed to meet promised capabilities.