Not exactly. It depends how energy is used: what portion.
If watts are used, or current, then yes you’re right.
But if mere volts are needed without any contribution from current, then no.
In other words, the controlling factor is the lifespan of the batteries and the lifespan of the magnet under the wear and tear of their use - not attributable to their expense of stored energy potential. No one has figured out how to get energy out of a magnet on a continual basis without ‘draining them’, so your analogies don’t apply. They’re not being drained the same way we drain batteries.
The contribution of the magnet is mostly wasted. A mere 7ppm in this simulation actually gets used. Since magnetism in a permanent magnet is not energy stored, but energy alignment, the loss over time is rated not on using up energy but using up its coherence. Coherence is not energy. It’s the intelligence of a magnet’s structure. We put that intelligence there using energy to do it. And energy gain is the result of using a magnet in a circuit in a manner to take advantage of the magnet’s coherence. So in a very real sense, we’re converting intelligence into energy, not one form of energy into another.
This is the other side of the story of electrodynamic theory left out of our view of the situation: that intelligence is just as significant as is energy (and energy’s equivalent version as matter). This is why I prefer to analyze electrical dynamics in terms of wave mechanics rather than ‘energy IN has to equal energy OUT’. For without energy, intelligence would have nothing to embody itself within. And without intelligence, energy would be a non-functional blob - very amorphous and not at all useful. This is analogous to my trying to make babies all on my own without the help of a woman contributing what I alone do not possess: the entire package of generation of life within my body.
Whereas zero point energy and energy from the vacuum are popular expressions, I don’t adhere to them. It’s far simpler: empty space - both inside matter/energy as well as devoid of them (theoretically, since we can’t separate the two in actuality) plus energy/matter comprise wave mechanics. So, I would have to differ with Newman on this point. E=MC2 of the copper and iron atoms are not the whole story. It’s how we use them that’s the other half of this story.