Regardless of one's views on climate change, running an air force by relying on refined fuel derived from black sticky gloop pumped out of the ground is not sustainable. There will, one day, be no crude oil left.
So there is a long term strategic benefit in finding a militarily viable alternative. There is also a short term strategic benefit, as one then doesn't end up relying on certain parts of the world with a propensity for instability. There is an even strong strategic benefit if it can be more or less entirely domestically produced. One is then pretty much proof against market manipulation, embargo, sanctions, blockade.
There are some things that tick this box. A hydrogen fueled economy can either lead to using H2 directly as a fuel in aircraft, or as part of a fuel synthesis industry. Such an economy might be powered by fission, fusion, and / or renewables.
Other things that might get there; the US once played with fission rockets, which was a pretty big failure. However, a fission reactor rocket using Americium makes a lot more sense - it'd be smaller, lighter, more robust, far less likely to emit radioactive contamination out the exhaust pipe.
As has been widely reported the Russians are toying with a nuclear powered hyper-sonic cruise missile. If they perfect that power plant, I shudder to think what else they might bolt it into.
I don't suppose the Chinese are sitting still either. Any student of warfare in the Pacific west knows that dependence on imported oil is not likely to result in prevailing in a military conflict.