Beam propulsion is impractical for aviation due to weather effects and line of sight. It's more than an engineering challenge, it just won't work (except for maybe a few limited cases of very short range flight in clear conditions).

You can beam from over the clouds (beaming antenna on a tethered balloon or even drone), and have a huge line of sight to boot.

It's an absolutely huge engineering challenge, but at least it doesn't require a discovery worth of the Nobel prize in chemistry (which I guess much improved batteries would warrant).

Having a huge line of sight doesn't solve the problem. The receiver has to be oriented roughly perpendicular to the incoming beam in order to get any reasonable efficiency. And the receiver has to be large in order to account for beam dispersion and aiming inaccuracy. For aerodynamic reasons the receiver can only be on the top or bottom of the aircraft and can't be angled much. So therefore the power transmitter must be close to directly above or below the aircraft.

Battery energy density is steadily improving every year. The 2019 Nobel Prize in Chemistry went to the inventors of the lithium ion battery.

https://www.nobelprize.org/prizes/chemistry/2019/press-relea...

I know some very smart people who are working on this. http://el-sky.com/

I wish them luck but I doubt they'll find a magic solution to beaming power through clouds.