What's the problem in designing a bright enough LED lamp?
The problem here is one of scale.

The way an LED works is that the electrons jump from the N side to the P side of the semiconductor junction, and as they do so some of the electrons fall into 'holes' in the P side.  This changes their energy level, and causes the discharge of a photon - ie, light.

This means that:


The junction is very small, so the amount of light emitted is limited.
Because the light comes from a very small area, it casts very sharp shadows.
As the light diffuses the 'quantity' of light in any one area drops massively, so what is bright in a tiny spot is dim in a large area.


Yes, you can have multiple LEDs in a 'bulb' to give a larger amount of light, and to provide a more diffuse shadow pattern, but still as the light diffuses it gets very much dimmer.  It then becomes a problem of sheer bulk - trying to get enough LEDs into a small enough area to give enough light at a reasonable distance.

That is why they work OK in a table lamp at close range, but at longer range (the ceiling) they are next to useless.