But afaik, solar panels currently convert only 20% of the energy to electricity, can you explain why this is close to the theoretically or practically possible maximum?
There's a theoretical limit of 55% for unconcentrated, 85% for concentrated sunlight. I'm not sure about the exact thermodynamical reasons for those numbers.
But claims of "1000x better" can physically never be true, unlike for batteries (e.g. antimatter, no matter how impractical, has millions times more energy density)
That a 528x improvement. If the price goes down in half again, quite possible with economies of scale, you have 1000x better in a significant measurement that counts.