why does an accelerated electric charge produce energy?
Do you mean why does an accelerated charge radiate?
yes, you're right~
This can only be seen in a detailed derivation of the radiation E and B fields.
See almost any intermediate or higher EM text.
The key point is that, for raditation, E and B fall off like 1/r instead of 1/r^2.
This follows from the use of the retarded time.
It turns out that if the velocity is constant, the retarded time does not result in the 1/r dependence.
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