Turns out, it has been done: https://www.youtube.com/watch?v=q2il8Fagbyk
They can theoretically made to be extremely large without much weight relative to the size. Which in turn allows you to accelerate even quite large payloads in a reasonable amount of time.
The flux even at earth orbit is a measly 47e-7 Newtons per square meter. That's 0.00016905632 pounds per square inch.
You still stand by what you just stated?
It's not feasible to do below clouds, in an environment with constant friction, air or water resistance.
The only reason you can do it in space is because that tiny slow acceleration can accumulate over a long period of time. This precludes frictional losses that would normally be incurred within atmospheres.
There is some work on the idea of using both a photon sail and a magnetic sail on a single vessel. In many interesting locations, these would push in different directions, allowing you to sail.
I suppose when your craft is big (or long) enough you could leverage differences in luminous flux (or intensity?) to generate some thrust. The differences will be tiny and the necessary craft size big. One would have to run the actual numbers, but it _could_ work in principle.
Compressing air by moving through it to leverage the resulting difference in velocities sadly won't work =( The steady state is then just the speed of air. I guess for light this also applies in a similar way.
It takes advantage of two things:
1) The Oberth effect, where thrust is more effective the deeper you go into a gravity well
2) The thrust from a solar increases as you get closer to the Sun