Your proposal violates the first law of thermodynamics, in that it requires wholesale creation of energy.

That is not possible. That is what is known as a perpetual motion device. They have been proposed and claimed many times.

There has never, and will never, be such a thing. In layman's terms, you can't make something out of nothing. You can't turn the chemical energy contained in one battery into heat, then mechanical work, then electricity, then mechanical work again, while somehow multiplying it.

In fact, the real world does the opposite- entropy and inefficiencies bleed some off at every conversion.

Which means simpler conversions are more efficient ones.

As for electric drive ships, they have been and are still built. The reason internal combustion prevails is because it is cheaper to operate, requires less space so more payload, is relatively efficient, and takes less crew, training and maintenance.