I don't see how balancing with each individual country makes sense.

Suppose for example the US needs to buy some natural resource from country X, which the US uses to build something that it sells to country Y at a very large profit. Suppose that the US doesn't export anything that country X needs or wants.

Balancing trade with X would mean cutting back on importing that natural resource, which would cut back on how much the US can build to sell to Y.

There will almost certainly also be loops in the graph of imports and exports. Things like A exports to B exports to C exports to A, with A, B, and C all having net balanced trade, but with each have a trade surplus with one of the others and a trade deficit with one.

If they all tried to force balanced trade with tariffs they just all end up paying more with no actual change in trade except possibly a reduction all around in the volume of trade.

This would be an optimization problem and there would need to be far more nuance. But the goal would be balance, without persistent overwhelming differences in trade deficits.