My question to You is... With infinite energy available, why does exchange need to be "balanced," and what does "balancing" it mean in practical terms?

One really good term, is the Propertarian term Reciprocity.

And it means as much as having your in breaths equal your out breaths.
If these are not in balance you get ill.

Wars are started over the buildup of inequality. Meaning, you aren't balancing your gives and gets. (not that we are all equal)

Further, you seem to envision these futuristic manufacturing centers that require no inputs.

They don't exist.

Lets take our toilet paper manufacturer.
It requires wood pulp (or hemp) and that requires trees. That requires growing trees, managing their growth and then harvesting. These are not things that robots are especially good at. Computer assisted, yes. Completely user free, no.

And that is just the first step, and there are many more.
Further, in the future, getting rid of all pollutants will be of utmost importance, and that takes time and atttention.

So, there will be a "family" that will spend much of its time growing the trees to manufacture the paper.

Of course this family should receive a balance of goods for its service.

Yes, electricity might be free, but human time is not.